Search results for: Green–Naghdi equations

Authors: Zarina Bibi, I., Khairil Iskandar, O.

Abstract:

In this paper, parallelism in the solution of Ordinary Differential Equations (ODEs) to increase the computational speed is studied. The focus is the development of parallel algorithm of the two point Block Backward Differentiation Formulas (PBBDF) that can take advantage of the parallel architecture in computer technology. Parallelism is obtained by using Message Passing Interface (MPI). Numerical results are given to validate the efficiency of the PBBDF implementation as compared to the sequential implementation.

Keywords: Ordinary differential equations, parallel.

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Authors: Javad Abdalkhani

Abstract:

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals..

Keywords: Nonlinear transformation, Abel Volterra Equations, Mathematica

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

Abstract:

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: Integral images, differential images, differential filters, image fusion.

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Authors: D. C. Lo, S. S. Leu

Abstract:

In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. The coupled equations are simultaneously solved by imposing the vorticity definition at boundary without requiring the explicit specification of the vorticity boundary conditions. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields. Thus, it is convinced that the present formulation is capable of solving coupled Navier-Stokes equations effectively and accurately.

Keywords: Natural convection, velocity-vorticity formulation, differential quadrature (DQ).

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Authors: Delfim Soares Jr.

Abstract:

In this work, a new family of time marching procedures based on Green’s function matrices is presented. The formulation is based on the development of new recurrence relationships, which employ time integral terms to treat initial condition values. These integral terms are numerically evaluated taking into account Newton-Cotes formulas. The Green’s matrices of the model are also numerically computed, taking into account the generalized-α method and subcycling techniques. As it is discussed and illustrated along the text, the proposed procedure is efficient and accurate, providing a very attractive time marching technique. 

Keywords: Dynamics, Time-Marching, Green’s Function, Generalized-α Method, Subcycling.

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Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: Close surfaces, high-order approach, numerical solutions, reaction-diffusion systems.

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Authors: Changqing Yang, Jianhua Hou

Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

Keywords: Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.

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Authors: Arti Vaish, Harish Parthasarathy

Abstract:

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.

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Authors: Fatemeh Cheraghali, Saeedeh Shojaee-Aliabadi, Seyede Marzieh Hosseini, Leila Mirmoghtadaie

Abstract:

In recent years, the field of natural antimicrobial and antioxidant compounds is one of the main research topics in the food industry. Application of agricultural residues is mainly cheap, and available resources are receiving increased attention. Walnut green husk is one of the agricultural residues that is considered as natural compounds with biological properties because of phenolic compounds. In this study, maltodextrin 10% was used for microencapsulation of walnut green husk extract. At first, the extract was examined to consider extraction yield, total phenolic compounds, and antioxidant activation. The results showed the extraction yield of 81.43%, total phenolic compounds of 3997 [mg GAE/100 g], antioxidant activity [DPPH] of 84.85% for walnut green husk extract. Antioxidant activity is about 75%-81% and by DPPH. At the next stage, microencapsulation was done by spry-drying method. The microencapsulation efficiency was 72%-79%. The results of SEM tests confirmed this microencapsulation process. In addition, microencapsulated and free extract was more effective on gram-positive bacteria’s rather than the gram-negative ones. According to the study, walnut green husk can be used as a cheap antioxidant and antimicrobial compounds due to sufficient value of phenolic compounds.

Keywords: Biopolymer, microencapsulation, Spray-drying, Walnut green husk.

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Authors: Janak Raj Sharma, Rajni Sharma

Abstract:

Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations.

Keywords: Nonlinear equations and systems, Newton's method, fixed point iteration, order of convergence.

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Authors: A. Mubarak, A. I. Augie

Abstract:

This study investigated the awareness level of green computing possessed by computer users in Kebbi state. Survey method was employed to carry out the study. The study involved computer users from ICT business/training centers around Argungu and Birnin Kebbi areas of Kebbi state. Purposive sampling method was used to draw 156 respondents that volunteer to answer the questionnaire administered for gathering the data of the study. Out of the 156 questionnaires distributed, 121 were used for data analysis. In all, 79 respondents were from Argungu, while 42 were from Birnin Kebbi. The two research questions of the study were answered with descriptive statistic (percentage), and inferential statistics (ANOVA). The findings showed that the most of the computer users do not possess adequate awareness on conscious use of computing system. Also, the study showed that there is no significant difference regarding the consciousness of green computing possesses among computer users in Argungu and Birnin Kebbi. Based on these findings, the study suggested among others an aggressive campaign on green computing practice among computer users in Kebbi state.

Keywords: Green computing, awareness, information technology, Energy Star.

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Authors: Kamyar Kabirifar, Majid Azarniush, Behbood Maashkar

Abstract:

A proper house is a suitable residential area which provides comfort, proper accessibility, security, stability and permanence of structure, enough lighting, proper initial infrastructures and ventilation for its inhabitants and the most important of all, it should be proportional to the family’s financial power .

Saving energy and making optimal usage of it and also taking advantage of stable energies are the bases of green buildings. Making green building will help the health of a person living in it and in its surrounding. It will support the people and provoke their satisfaction. Not only it will bring about the raise of level of the quality of life for building inhabitants, but it will cause the promotion of quality level of life of the people living in the surrounding area and in general the society. 

 

Keywords: Quality of Life, Green Building, environment pollution, Sick Building.

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Authors: Juliana C. Alencar, Monica Ferreira do Amaral Porto

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The blue-green infrastructure in recent years has been pointed out as a possibility to increase the environmental quality of watersheds. The regulation ecosystem services brought by these areas are many, such as the improvement of the air quality of the air, water, soil, microclimate, besides helping to control the peak flows and to promote the quality of life of the population. This study proposes a blue-green infrastructure scenario for the Jaguaré watershed, located in the western zone of the São Paulo city in Brazil. Based on the proposed scenario, it was verified the impact of the adoption of the blue and green infrastructure in the control of the peak flow of the basin, the benefits for the avifauna that are also reflected in the flora and finally, the quantification of the regulation ecosystem services brought by the adoption of the scenario proposed. A survey of existing green areas and potential areas for expansion and connection of these areas to form a network in the watershed was carried out. Based on this proposed new network of green areas, the peak flow for the proposed scenario was calculated with the help of software, ABC6. Finally, a survey of the ecosystem services contemplated in the proposed scenario was made. It was possible to conclude that the blue and green infrastructure would provide several regulation ecosystem services for the watershed, such as the control of the peak flow, the connection frame between the forest fragments that promoted the environmental enrichment of these fragments, improvement of the microclimate and the provision of leisure areas for the population.

Keywords: Blue and green infrastructure, sustainable drainage, urban waters, ecosystem services.

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Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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Authors: T. G. Emam

Abstract:

The effect of variable chemical reaction on heat and mass transfer characteristics over unsteady stretching surface embedded in a porus medium is studied. The governing time dependent boundary layer equations are transformed into ordinary differential equations containing chemical reaction parameter, unsteadiness parameter, Prandtl number and Schmidt number. These equations have been transformed into a system of first order differential equations. MATHEMATICA has been used to solve this system after obtaining the missed initial conditions. The velocity gradient, temperature, and concentration profiles are computed and discussed in details for various values of the different parameters.

Keywords: Heat and mass transfer, stretching surface, chemical reaction, porus medium.

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Authors: Mao Wei

Abstract:

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.

Keywords: Stochastic age-dependent population equations, poisson random measures, numerical solutions, exponential stability.

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Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam

Abstract:

Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.

Keywords: Heat conduction, Cellular automata, convergencerate, discrete system.

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Authors: İlke Bereketli, Müjde Erol Genevois, H. Ziya Ulukan

Abstract:

Nowadays, manufacturers are facing great challenges with regard to the production of green products due to the emerging issue of hazardous substance management (HSM). In particular, environmental legislation pressures have yielded to increased risk, manufacturing complexity and green components demands. The green principles were expanded to many departments within organization, including supply chain. Green supply chain management (GSCM) was emerging in the last few years. This idea covers every stage in manufacturing from the first to the last stage of life cycle. From product lifecycle concept, the cycle starts at the design of a product. QFD is a customer-driven product development tool, considered as a structured management approach for efficiently translating customer needs into design requirements and parts deployment, as well as manufacturing plans and controls in order to achieve higher customer satisfaction. This paper develops an Eco- QFD to provide a framework for designing Eco-mobile phone by integrating the life cycle analysis LCA into QFD throughout the entire product development process.

Keywords: Eco-design, Eco-QFD, EEE, Environmental New Product Development, Mobile Phone.

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Authors: A. M. Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: N. Fusun Oyman Serteller

Abstract:

In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: Finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations.

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Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

Abstract:

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: A. S. Kipcak, O. Dere Ozdemir, E. Moroydor Derun, M. B. Piskin

Abstract:

Tea has several types of essential elements. Potassium, magnesium and phosphorus are some examples of these elements. Tea is widely used drink in Turkey, also some people puts a lemon wedge to tea for different taste. In this study potassium, magnesium and phosphorus contents after the hot water brewing of black and green tea were determined by Optical Emission Spectroscopy (ICPOES). Furthermore, how the lemon addition to teas affects the concentrations of the potassium, magnesium and phosphorus amount are investigated. From the results, potassium, magnesium and phosphorus concentrations are found as 3003.3, 597.1, 1167.2 ppm in black tea and 3718.0, 3830.5, 376.4 ppm in green tea, respectively. After lemon addition potassium, magnesium and phosphorus concentrations are changed to 14930, 830.4, 1113.5 ppm in black tea and 15460.0, 909.5, 1152.5 ppm in green tea, respectively. It is seen that lemon addition affects some essential elements in black and green Turkish teas.

Keywords: Hot water brewing, ICP-OES, lemon, tea

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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Authors: R. B. Ogunrinde

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: Differential equations, Numerical, Initial value problem, Polynomials.

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Authors: Phool Singh, Ashok Jangid, N.S. Tomer, Deepa Sinha

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The aim of this paper is to study the oblique stagnation point flow on vertical plate with uniform surface heat flux in presence of magnetic field. Using Stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained using Runge-Kutta Fehlberg method with the help of shooting technique. In the present work the effects of striking angle, magnetic field parameter, Grashoff number, the Prandtl number on velocity and heat transfer characteristics have been discussed. Effect of above mentioned parameter on the position of stagnation point are also studied.

Keywords: Heat flux, Oblique stagnation point, Mixedconvection, Magneto hydrodynamics

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Authors: Nickson Kipng’etich Lang’at, Thomas Thoruwa, John Abraham, John Wanyoko

Abstract:

Green tea is made from the top two leaves and buds of a shrub, Camellia sinensis, of the family Theaceae and the order Theales. The green tea leaves are picked and immediately sent to be dried or steamed to prevent fermentation. Fluid bed drying technique is a common drying method used in drying green tea because of its ease in design and construction and fluidization of fine tea particles. Major problems in this method are significant loss of chemical content of the leaf and green appearance of tea, retention of high moisture content in the leaves and bed channeling and defluidization. The energy associated with the drying technology has been shown to be a vital factor in determining the quality of green tea. As part of the implementation, prototype dryer was built that facilitated sequence of operations involving steaming, cooling, pre-drying and final drying. The major findings of the project were in terms of quality characteristics of tea leaves and energy consumption during processing. The optimal design achieved a moisture content of 4.2 ± 0.84%. With the optimum drying temperature of 100 ºC, the specific energy consumption was 1697.8 kj.Kg^-1 and evaporation rate of 4.272 x 10^-4 Kg.m^-2.s^-1. The energy consumption in a fluidized system can be further reduced by focusing on energy saving designs.

Keywords: Evaporation rate, fluid bed dryer, maceration, specific energy consumption.

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Authors: S. Damodaran, T. V. S.Sekhar

Abstract:

The motion of a sphere moving along the axis of a rotating viscous fluid is studied at high Reynolds numbers and moderate values of Taylor number. The Higher Order Compact Scheme is used to solve the governing Navier-Stokes equations. The equations are written in the form of Stream function, Vorticity function and angular velocity which are highly non-linear, coupled and elliptic partial differential equations. The flow is governed by two parameters Reynolds number (Re) and Taylor number (T). For very low values of Re and T, the results agree with the available experimental and theoretical results in the literature. The results are obtained at higher values of Re and moderate values of T and compared with the experimental results. The results are fourth order accurate.

Keywords: Navier_Stokes equations, Taylor number, Reynolds number, Higher order compact scheme, Rotating Fluid.

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Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar

Abstract:

This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.

Keywords: Generalized projective synchronization; Fractionalorder;Chaos; Caputo derivative; Differential transform method

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Authors: Lv Yuhua

Abstract:

In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results  (see[5,6]), and the results is new even in finite dimensional spaces.

Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.

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