Search results for: settlement equations

Authors: Mawarni Mohamed, Sharifah Shahira A. Hamid

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Leisure time is an important component to offset the sedentary lifestyle of the people. Women tend to benefit from leisure activities not only to reduce stress but also to provide opportunities for well-being and self-satisfaction. This study was conducted to investigate body composition and leisure time use among women in Selangor from the influences of community settlement. A total of 419 women aged 18-65 years were selected to participate in this study. Descriptive statistics, t-test and ANOVA were used to analyze the level of physical activity and the relationship between leisure-time use and body composition were made to analyze the physical lifestyles. The results showed that women with normal body composition seem to be involved in more passive activities than women with less weight gain and obesity. Thus, the study recommended that the government and other health and recreational agencies should develop more places and activities suitable for leisure preference for women in their community settlement so they become more interested to engage in more active recreational and physical activities.

Keywords: body composition, community settlement, leisure time, physical lifestyles

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Authors: Sateesh Kumar Pisini, Swetha Priya Darshini Thammadi, Sanjay Kumar Shukla

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Granular piles are a popular ground improvement technique in soft cohesive soils as well as for loose non-cohesive soils. The present experimental study has been carried out on granular piles in loose (Relative density = 30%) and medium dense (Relative density = 60%) sands with geogrid reinforcement within the sand bed over the granular piles. A group of five piles were installed in the sand at different spacing, s = 2d, 3d and 4d, d being the diameter of the pile. The length (L = 0.4 m) and diameter (d = 50 mm) of the piles were kept constant for all the series of experiments. The load-settlement behavior of reinforced sand bed and granular piles system was studied by applying the load on a square footing. The results show that the effect of reinforcement increases the load bearing capacity of the piles. It is also found that an increase in spacing between piles decreases the settlement for both loose and medium dense soil.

Keywords: granular pile, load-carrying capacity, settlement, geogrid reinforcement, sand

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Authors: Bashir Ahmad Amiri, Nsenda Lukumwena

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The developing economies are experiencing an unprecedented rate of urbanization, mainly the urbanization of poverty which is leading to sprawling of slums and informal settlement. Kabul, being the capital and primate city of Afghanistan is grossly encountered to the informal settlement where the majority of the people consider to be informal. Despite all efforts to upgrade and minimize the growth of these settlements, they are growing rapidly. Various interventions have been taken by the government and some international organizations from physical upgrading to urban renewal, but none of them have succeeded to solve the issue of informal settlement. The magnitude of the urbanization and the complexity of informal settlement in Kabul city, and the institutional and capital constraint of the government calls for integration and optimization of currently practiced strategies. This paper provides an overview of informal settlement formation and the conventional upgrading strategies in Kabul city to identify the dominant/successful practices and rationalize the conventional upgrading modes. For this purpose, Hothkhel has been selected as the case study, since it represents the same situation of major informal settlements of the city. Considering the existing potential and features of the Hothkhel and proposed land use by master plan this paper intends to find a suitable upgrading mode for the study area and finally to scale up the model for the city level upgrading. The result highlights that the informal settlements of Kabul city have high (re)development capacity for accepting the additional room without converting the available agricultural area to built-up. The result also indicates that the integrated multi-sector upgrading has the scale-up potential to increase the reach of beneficiaries and to ensure an inclusive and efficient urbanization.

Keywords: informal settlement, upgrading strategies, Kabul city, urban expansion, integrated multi-sector, scale-up

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Authors: Kamel Al-Khaled

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Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

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Authors: Zenebu Adere Tola

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Informal settlements behave dynamically over space and time and the number of people living in such housing areas is growing worldwide. In the cities of developing countries especially in sub-Saharan Africa, poverty, unemployment rate, poor living condition, lack transparency and accountability, lack of good governance are the major factors to contribute for the people to hold land informally and built houses for residential or other purposes. In most of Ethiopian cities informal settlement is highly seen in peripheral areas this is because people can easily to hold land for housing from local farmers, brokers, speculators without permission from concerning bodies. In Adama informal settlement has created risky living conditions and led to environmental problems in natural areas the main reason for this was the lack of sufficient knowledge about informal settlement development. On the other side there is a strong need to transform informal into formal settlements and to gain more control about the actual spatial development of informal settlements. In another hand to tackle the issue it is at least very important to understand the scale of the problem. To understand the scale of the problem it is important to use up-to-date technology. For this specific problem, it is good to use high-resolution imagery to detect informal settlement in Adama city. The main objective of this study is to assess the spatiotemporal dynamics and environmental impacts of informal settlement using OBIA. Specifically, the objective of this study is to; identify informal settlement in the study area, determine the change in the extent and pattern of informal settlement and to assess the environmental and social impacts of informal settlement in the study area. The methods to be used to detect the informal settlement is object-oriented image analysis. Consequently, reliable procedures for detecting the spatial behavior of informal settlements are required in order to react at an early stage to changing housing situations. Thus, obtaining spatial information about informal settlement areas which is up to date is vital for any actions of enhancement in terms of urban or regional planning. Using data for this study aerial photography for growth and change of informal settlements in Adama city. Software ECognition software for classy to built-up and non-built areas. Thus, obtaining spatial information about informal settlement areas which is up to date is vital for any actions of enhancement in terms of urban or regional planning.

Keywords: informal settlement, change detection, environmental impact, object based analysis

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Authors: John Abubakar

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Access to decent housing is a global challenge. An estimated one billion people currently live in slum settlements globally. About 80 percent of these slum dwellers are in Asia and Africa. Nigeria accounts for a significant percentage of African slum dwellers because of its size. Addressing the challenge of slum settlement in Nigeria can have far reaching positive implications in Africa. A major slum settlement in Nigeria is Mararaba slum in Karu local government of Nasarawa state. The importance of this slum settlement hinges on its proximity to Abuja, Nigeria’s capital city. This study is an attempt at identifying the impact of self-help housing and government mass housing scheme in addressing the problem of housing access in Mararaba area of Karu local government, Nasarawa state. The research method used is the content analysis of existing literature. After the review of existing literature, the paper argues that self-help house is more impactful in addressing housing access in Mararaba area of Karu local government. Therefore, self-help housing should be recognized and incorporated into the housing policy of Nasarawa state. Both self-help housing and government mass housing programs are reviewed comparatively, and their strengths and weaknesses analyses.

Keywords: slum settlement, informal settlement, progressive improvement, holistic planning

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Authors: Shenpu Liu

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Space syntax, a paradigm of the urban research, which manifests people’s intuitive and abstract perception of a material space with a solid mathematical way, explores how space represents its social characteristics. Taking Xiazhuang village and Shijia Village in Huzhou as an example and focusing on inward structure and street space, this article recognizes the connotative significance of the settlement with the aid of space syntax theory and quantitative analysis method from the perspective of spatial configuration to present relevant suggestions for its future planning and provides references for traditional rural settlement protection.

Keywords: Shijia village, space configuration, space syntax, traditional rural settlement, Xiazhuang village

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Authors: Yusuf Sani Abubakar

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This paper investigates mechanisms of settlement of disputes at the Islamic Financial Institutions (IFIs). Dispute settlement at the Islamic Financial Institutions (IFIs) can be both through litigation as well as Alternative Dispute Resolution (ADR). The paper aims to investigate how disputes are settled at the Islamic Financial Institutions (IFIs), as it is natural to have disagreements between different parties involved in the business of Islamic Financial Institutions (IFIs). The paper adopts a qualitative methodology where the sources are taken from journals, books, websites etc. In analyzing the data obtained from the sources, content analysis will be used. In addition to writings on this topic by various writers, this paper will add to the literature and will recommend certain effective ways of solving disputes arising between parties participating in the business of Islamic Financial Institutions (IFIs).

Keywords: Islamic finance, dispute resolution, Islamic financial institutions, litigation

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: M. L. Burnwal, P. Raychowdhury

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Earthquake leads to adverse effects on buildings resting on soft soils. Mitigating the response of shallow foundations on soft soil with different methods reduces settlement and provides foundation stability. Few methods such as the rocking foundation (used in Performance-based design), deep foundation, prefabricated drain, grouting, and Vibro-compaction are used to control the pore pressure and enhance the strength of the loose soils. One of the problems with these methods is that the settlement is uncontrollable, leading to differential settlement of the footings, further leading to the collapse of buildings. The present study investigates the utility of geosynthetics as a potential improvement of the subsoil to reduce the earthquake-induced settlement of structures. A steel moment-resisting frame building resting on loose liquefiable dry soil, subjected to Uttarkashi 1991 and Chamba 1995 earthquakes, is used for the soil-structure interaction (SSI) analysis. The continuum model can simultaneously simulate structure, soil, interfaces, and geogrids in the OpenSees framework. Soil is modeled with PressureDependentMultiYield (PDMY) material models with Quad element that provides stress-strain at gauss points and is calibrated to predict the behavior of Ganga sand. The model analyzed with a tied degree of freedom contact reveals that the system responses align with the shake table experimental results. An attempt is made to study the responses of footing structure and geosynthetics with unreinforced and reinforced bases with varying parameters. The result shows that geogrid reinforces shallow foundation effectively reduces the settlement by 60%.

Keywords: settlement, shallow foundation, SSI, continuum FEM

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Authors: Tahsin Toma Sabbagh, Ihsan Al-Abboodi, Ali Al-Jazaairry

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Allowable-bearing capacity is the competency of soil to safely carries the pressure from the superstructure without experiencing a shear failure with accompanying excessive settlements. Ensuring a safe bearing pressure with respect to failure does not tolerate settlement of the foundation will be within acceptable limits. Therefore, settlement analysis should always be performed since most structures are settlement sensitive. When visualising the movement of a soil wedge in the bearing capacity criterion, both vertically and horizontally, it becomes clear that by confining the soil surrounding the foundation, both the bearing capacity and settlement values improve. In this study, two sizes of spread foundation were considered; (2×4) m and (3×5) m. These represent two real problem case studies of an existing building. The foundations were analysed in terms of dimension as well as position with respect to a confining wall (i.e., sheet piles on both sides). Assuming B is the least foundation dimension, the study comprised the analyses of three distances; (0.1 B), (0.5 B), and (0.75 B) between the sheet piles and foundations alongside three depths of confinement (0.5 B), (1 B), and (1.5 B). Nonlinear three-dimensional finite element analysis (ANSYS) was adopted to perform an analytical investigation on the behaviour of the two foundations contained by the case study. Results showed that confinement of foundations reduced the overall stresses near the foundation by 65% and reduced the vertical displacement by 90%. Moreover, the most effective distance between the confinement wall and the foundation was found to be 0.5 B.

Keywords: bearing capacity, cohesionless soils, soil confinement, soil modelling, spread footings

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Divij Gupta

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Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: Abdelazim Makki Ibrahim, Esamaldeen Ali

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This study aims at analysing the load settlement behavior and predict the bearing capacity of piled raft foundation a series of finite element models with different foundation configurations and stiffness were established. Numerical modeling is used to study the behavior of the piled raft foundation due to the complexity of piles, raft, and soil interaction and also due to the lack of reliable analytical method that can predict the behavior of the piled raft foundation system. Simple analytical models are developed to predict the average settlement and the load sharing between the piles and the raft in piled raft foundation system. A simple example to demonstrate the applications of these charts is included.

Keywords: finite element, pile-raft foundation, method, PLAXIS software, settlement

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Authors: Shuo Wang

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The hydrogeological parameters of the engineering site and the hydraulic connection between the aquifers can be obtained by the pumping test. Through the recovery test, the characteristics of water level recovery and the law of surface subsidence recovery can be understood. The above two tests can provide the basis for subsequent engineering design. At present, the deformation of deep soil caused by pumping tests is often neglected. However, some studies have shown that the maximum settlement subject to groundwater drawdown is not necessarily on the surface but in the deep soil. In addition, the law of settlement recovery of each soil layer subject to water level recovery is not clear. If the deformation-sensitive structure is deep in the test site, safety accidents may occur. In this study, the pumping test and recovery test of a confined aquifer in Shanghai are introduced. The law of measured groundwater changes and surface subsidence are analyzed. In addition, the fluid-solid coupling model was established by ABAQUS based on the Biot consolidation theory. The models are verified by comparing the computed and measured results. Further, the variation law of water level and the deformation law of deep soil during pumping and recovery tests under different site conditions and different times and spaces are discussed through the above model. It is found that the maximum soil settlement caused by pumping in a confined aquifer is related to the permeability of the overlying aquitard and pumping time. There is a lag between soil deformation and groundwater changes, and the recovery rate of settlement deformation of each soil layer caused by the rise of water level is different. Finally, some possible research directions are proposed to provide new ideas for academic research in this field.

Keywords: coupled hydro-mechanical analysis, deep ground settlement, numerical simulation, pumping test, recovery test

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Authors: Feicheng Liu, Weiming Liao, Jianjing Zhang

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A pile-supported embankment with geosynthetic-reinforced mat (PSGR embankment) has been considered as an effective solution to reduce the total and differential settlement of the embankment constructed over soft soil. In this paper, a new simplified method proposed firstly incorporates the load transfer between piles and surrounding soil and the settlement of pile, and also considers arching effect in embankment fill, membrane effect of geosynthetic reinforcement, and subsoil resistance, to evaluate the behavior of PSGR embankment. Subsoil settlement is assumed to consist of two parts:(1) the settlement of subsoil surface between piles equivalent to that of pile caps assuming the geosynthetic reinforcement without deformation yet; (2) the subsoil subsiding along with the geosynthetic deforming, and the deflected geosynthetic being considered as centenary. The force equilibrium, including loads acting on the upper surface of geosynthetic, subsoil resistance, as well as the stress-strain relationship of the geosynthetic reinforcement at the edge of pile cap, is established, thus the expression of subsoil resistance is deduced, and subsequently the tension of geosynthetic and stress concentration ratio between piles can be calculated. The proposed method is validated through observed data from three field tests and also compared with other eight analytical solutions available in the literature. In addition, a sensitive analysis is provided to demonstrate the influence of with/without considering pile-soil interaction for evaluating the performance of PSGR embankment.

Keywords: pile-supported embankment, geosynthetic, analytical solution, soil arching effect, the settlement of pile, sensitive analysis

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Authors: Anjana R. Menon, Anjana Bhasi

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This paper deals with the numerical analysis of Prefabricated Horizontal Drain (PHD) induced consolidation of clayey deposits, using ABAQUS. PHDs are much like Prefabricated Vertical Drains (PVDs) installed in horizontal layers, used mainly for enhancing the consolidation of clayey fill embankments, and dredged mud deposits. The efficiency of the system depends mainly on the spacing and layout of the drain. Hence, two spacing related parameters are defined, namely WH (width to horizontal spacing ratio) and VH (vertical to horizontal spacing ratio), and the finite element models are developed based on plane strain unit cell conditions under various combinations of these parameters. The analysis results, in terms of degree of consolidation (U), are compared with the established theories. Based on the analysis, a set of equations are proposed to analyse the PHD induced consolidation. The proposed method is found to be reasonably accurate. Further, the effect of PHDs at different spacing ratios, in accelerating consolidation of a clayey embankment fill is analysed in terms of pore pressure dissipation rate, and settlement. The PHD is found to accelerate the rate of pore pressure dissipation by more than 50%, thus reducing the time for final settlement significantly.

Keywords: ABAQUS, consolidation, plane strain, prefabricated horizontal drain

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Mehrnaz Alibeikloo, Hadi Khabbaz, Behzad Fatahi

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The spectral random field method is one of the widely used methods to obtain more reliable and accurate results in geotechnical problems involving material variability. Karhunen-Loeve (K-L) expansion method was applied to perform random field discretization of cross-correlated creep parameters. Karhunen-Loeve expansion method is based on eigenfunctions and eigenvalues of covariance function adopting Kernel integral solution. In this paper, the accuracy of Karhunen-Loeve expansion was investigated to predict long-term settlement of soft soils adopting elastic visco-plastic creep model. For this purpose, a parametric study was carried to evaluate the effect of K-L expansion terms and spatial correlation length on the reliability of results. The results indicate that small values of spatial correlation length require more K-L expansion terms. Moreover, by increasing spatial correlation length, the coefficient of variation (COV) of creep settlement increases, confirming more conservative and safer prediction.

Keywords: Karhunen-Loeve expansion, long-term settlement, reliability analysis, spatial correlation length

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Authors: Waqed H. Almohammed, Mohammed Y. Fattah, Sajjad E. Rasheed

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Dynamic traffic loads cause deformation of underground pipes, resulting in vehicle discomfort. This makes it necessary to reinforce the layers of soil above underground pipes. In this study, the subbase layer was reinforced. Finite element software (PLAXIS 3D) was used to in the simulation, which includes geocell reinforcement, vehicle loading, soil layers and Glass Fiber Reinforced Plastic (GRP) pipe. Geocell reinforcement was modeled using a geogrid element, which was defined as a slender structure element that has the ability to withstand axial stresses but not to resist bending. Geogrids cannot withstand compression but they can withstand tensile forces. Comparisons have been made between the numerical models and experimental works, and a good agreement was obtained. Using the mathematical model, the performance of three different pipes of diameter 600 mm, 800 mm, and 1000 mm, and three different vehicular speeds of 20 km/h, 40 km/h, and 60 km/h, was examined to determine their impact on surface settlement and vertical pressure at the pipe crown for two cases: with and without geocell reinforcement. The results showed that, for a pipe diameter of 600 mm under geocell reinforcement, surface settlement decreases by 94 % when the speed of the vehicle is 20 km/h and by 98% when the speed of the vehicle is 60 km/h. Vertical pressure decreases by 81 % when the diameter of the pipe is 600 mm, while the value decreases to 58 % for a pipe with diameter 1000 mm. The results show that geocell reinforcement causes a significant and positive reduction in surface settlement and vertical stress above the pipe crown, leading to an increase in pipe safety.

Keywords: dynamic loading, finite element, geocell-reinforcement, GRP pipe, PLAXIS 3D, surface settlement

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Authors: Shu-Yen Wang, Shyh-Huei Hwang

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Designated as an important architectural complex of settlement by the Ministry of Culture, Hua-Zhai Settlement located in Wang-An Township, Peng-Hu County, of Taiwan has been progressively restored year by year and is now at the revitalization and reutilization stage. Over the last 5 years, YunTech has participated in the restoration project while being in compliance with the Bureau of Cultural Heritage’s spirit of 'Living Heritage Conservation'. In this study, reflections have been made to evaluate the contemporariness of traditional settlement development from the aspects of revitalization and reutilization. On the one hand, the connection between settlers’ experiences and emotions have been clarified through the living nodes, collective memory, and social-cultural connotation. On the other hand, activity design has promoted the reconstruction of living nodes and facilitated the reconnection of collective memory, enabling us to explore the contemporariness of living nodes after the reconstruction. With the adoption of literature review, participant observation, and interview analysis methods, this study concludes the following results: 1) The node reconstruction brings back the memories and makes emotional connections: the spatial collective memory is composed of different components. During the reconstruction of node space, villagers participated not only in the narration of the history but also in the restoration of the space. This process enables villagers to bring back their memories and make emotional connections thereto. 2) Villagers’ understanding towards revitalization has been facilitated through node reconstruction: as a medium of this project, activity design has facilitated node reconstruction by offering villagers a natural environment to build up emotional connections to the settlement. This also enables us to better understand the meaning of settlement activation for the local community. 3) New connections are established in life between villagers and the university through the construction of living nodes: through the local implementation of node reconstruction, new connections have been established in life between villagers who participated in the project and the university. In the meantime, the university’s entrance to the community has also been revalued.

Keywords: collective memory, local sense of belonging, reconstruction of living nodes, the important architectural complex of Wang-An Hua-Zhai settlement

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Magigi Wakuru, Gaudensi Kapinga

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This study examines land use changes and its implications on livelihood activities of peri-urban settlements in Msaranga, Moshi Municipality. Specifically; it analyses the historical development of the settlement, socioeconomic characteristics and land use changes over time. Likely, find out existing livelihood activities and how have been changing over time in the context of urbanization, and lastly highlights land use change implications on livelihood activities to residents. Interviews, observations, documentary reviews and mapping were data collection tools employed. The study shows that housing, urban agriculture, roads infrastructure, recreational, open spaces and institutions are some land use types existing in the settlement. On-farm and off-farm livelihood activities have been identified livelihood activities in the settlement. These include crop cultivation, livestock keeping, trading and formal employment and have been changing over time. However, urbanisation observed to be a catalyst of change and affect livelihood activities over time. Resorting to off-farm livelihoods activities including engaging in retail business and seeking employment in formal and informal sector are some copying strategies documented. The study wind up by pointing roles of different actors and issues of particular attention to different stakeholders towards reducing impact of land use changes on livelihood strategies in the settlement. Likely, unresolved issues for future research and policy development agenda are highlighted in this study. The study concludes that the impact of land use changes on livelihood activities need collaborative effort of different stakeholders, policy enforcement as well as public private partnership in issues based implementation in cities like Moshi where land use is rapidly changing over time within urban planning cycles due to increasing population demand in cities of Sub-Saharan Africa.

Keywords: land use, land use changes, livelihood activities, peri-urban settlement, Moshi, Tanzania

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Baghdad Said

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Differential equations of fractional order have proved to be important tools to describe many physical phenomena and have been used in diverse fields such as engineering, mathematics as well as other applied sciences. On the other hand, the theory of differential equations involving the Stieltjes derivative (SD) with respect to a non-decreasing function is a new class of differential equations and has many applications as a unified framework for dynamic equations on time scales and differential equations with impulses at fixed times. The aim of this paper is to investigate the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability (UHRS) of solutions for a boundary value problem of sequential fractional differential equations (SFDE) containing (SD). This study is based on the technique of noncompactness measures (MNCs) combined with Monch-Krasnoselski fixed point theorems (FPT), and the results are proven in an appropriate Banach space under sufficient hypotheses. We also give an illustrative example. In this work, we introduced a class of (SFDE) and the results are obtained under a few hypotheses. Future directions connected to this work could focus on another problem with different types of fractional integrals and derivatives, and the (SD) will be assumed under a more general hypothesis in more general functional spaces.

Keywords: SFDE, SD, UHRS, MNCs, FPT

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Authors: Zhanar Imanova

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Masses of real celestial bodies change anisotropically and reactive forces appear, and they need to be taken into account in the study of these bodies' dynamics. We studied the two-planet problem of three bodies with variable masses in the presence of reactive forces and obtained the equations of perturbed motion in Newton’s form equations. The motion equations in the orbital coordinate system, unlike the Lagrange equation, are convenient for taking into account the reactive forces. The perturbing force is expanded in terms of osculating elements. The expansion of perturbing functions is a time-consuming analytical calculation and results in very cumber some analytical expressions. In the considered problem, we obtained expansions of perturbing functions by small parameters up to and including the second degree. In the non resonant case, we obtained evolution equations in the Newton equation form. All symbolic calculations were done in Wolfram Mathematica.

Keywords: two-planet, three-body problem, variable mass, evolutionary equations

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