Search results for: integral equation approach

Authors: Ka C. Lam, Oluwafunmibi S. Idowu

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Building girth is important in building economics and mostly used in quantities take-off of various cost items. Literature suggests that the use of conceptual quantities can improve the accuracy of cost models. Girth or perimeter of a building can be used to estimate conceptual quantities. Hence, the current paper aims to model the perimeter-area function of buildings shapes for use at the conceptual design stage. A detailed literature review on existing building shape indexes was carried out. An empirical approach was used to study the relationship between area and the shortest length of a four-sided orthogonal polygon. Finally, a mathematical approach was used to establish the observed relationships. The empirical results obtained were in agreement with the mathematical model developed. A new equation termed “conceptual perimeter equation” is proposed. The equation can be used to estimate building envelope quantities such as external wall area, external finishing area and scaffolding area before sketch or detailed drawings are prepared.

Keywords: building envelope, building shape index, conceptual quantities, cost modelling, girth

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Authors: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena.

Keywords: deep learning, optical soliton, physics informed neural network, partial differential equation

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Samson Davoyan, Ashot Davoyan, Ani Khachatryan

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The indexes (Global Competitiveness Index, Economic Freedom Index, Human Development Index, etc.) developed by different international and non-government organizations in time and space express the quantitative and qualitative features of different fields of various reforms implemented in different countries. The main objective of our research is to develop new methodology that we will use to create integral index based on many indexes and that will include many areas of reforms. To achieve our aim we have used econometric methods (regression model for panel data method). The basis of our methodology is the development of the new integral index based on quantitative assessment of the change of two main parameters: the score of the countries by different indexes and the change of the ranks of countries for following two periods of time. As a result of the usage of methods for analyzes we have defined the indexes that are used to create the new integral index and the scales for each of them. Analyzing quantitatively and qualitatively analysis through the integral index for more than 100 countries for 2009-2014, we have defined comparative efficiency that helps to conclude in which directions countries have implemented reforms more effectively compared to others and in which direction reforms have implemented less efficiently.

Keywords: development, rank, reforms, comparative, index, economic, corruption, social, program

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Authors: Chor Nejmeddine, Ines Ben Omrane, Mohamed Abdelwahed

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In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.

Keywords: heat equation, spectral elements discretization, error indicators, Euler

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: Sanjay Kumar, Lillie Dewan

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The study of complex dynamic systems has advanced through various scientific approaches with the help of computer modeling. The common design trends in aerospace system design can be applied to quadcopter design. A quadcopter is a nonlinear, under-actuated system with complex aerodynamics parameters and creates challenges that demand new, robust, and effective control approaches. The flight control stability can be improved by planning and tracking the trajectory and reducing the effect of sensors and the operational environment. This paper presents a modern design Simmechanics visual modeling approach for a mechanical model of a quadcopter with three degrees of freedom. The Simmechanics model, considering inertia, mass, and geometric properties of a dynamic system, produces multiple translation and rotation maneuvers. The proportional, integral, and derivative (PID) controller is integrated with the Simmechanics model to follow a predefined quadcopter rotational trajectory for a fixed time interval. The results presented are satisfying. The simulation of the quadcopter control performed operations successfully.

Keywords: nonlinear system, quadcopter model, simscape modelling, proportional-integral-derivative controller

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Authors: Weiping Liu

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This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods.

Keywords: stock price, multistage model, different growth model, discounted cash flow method

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Authors: Themistoklis Tzimas

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The proposed paper focuses on a triangular relationship, between human security, human development and responsibility to rebuild. This relationship constitutes the innovative contribution to the debate about human security. Human security constitutes a generic and legally binding notion, which orientates from an integrated approach the UN Charter principles and of the collective security system. Such an approach brings at the forefront of international law and of international relations not only states but non- state actors as well. Several doctrines attempt to implement the fore-mentioned approach among which the Responsibility to Protect- hereinafter R2P- doctrine and its aspect of Responsibility to Rebuild- hereinafter R2R. In this sense, R2P in general and R2R are supposed to be guided by human security imperatives. Human security because of its human- centered approach encompasses as an integral part of it, human development. Human development constitutes part of the backbone of human security, since it deals with the social and economic root- causes of the threats, which human security attempts to confront. In this sense, doctrines which orientate from human security, such as R2P and its R2R aspect should also take into account human development imperatives, in order to improve their efficiency. On the contrary though, R2R is more often linked with market- orientated policies, which are often imposed under transitional authorities, regardless of local needs. The implementation of such policies can be identified as a cause for striking failures in the framework of R2R. In addition it is a misinterpretation of the essence of human security and subsequently of R2P as well. The findings of the article, on the basis of the fore-mentioned argument is that a change must take place from a market- orientated misinterpretation of R2R to an approach attempting to implement human development doctrines, since the latter lie at the heart of human security and can be proven more effective in dealing with the root- causes of conflicts. Methodologically, the article begins with an examination of human security and of its binding nature on the basis of its orientation from the UN Charter. It also examines its significance in the framework of the collective security system. Then, follows the analysis of why and how human development constitutes an integral part of human security. At the next part it is proven that R2P in general and R2R more specifically constitute or should constitute an attempt to implement human security doctrines within the collective security system. Having built this triangular relationship it is argued that human development is proven to be the most suitable notion, so that the spirit of human security and the scopes of R2P are successfully implemented.

Keywords: human security, un charter, responsibility to protect, responsibility to rebuild, human development

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Authors: Gulcan Ozerim, Gunay Anlas

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In shape memory alloys, upon loading, stress increases around crack tip and a martensitic phase transformation occurs in early stages. In many studies the stress distribution in the vicinity of the crack tip is represented by using linear elastic fracture mechanics (LEFM) although the pseudo-elastic behavior results in a nonlinear stress-strain relation. In this study, the HRR singularity (Hutchinson, Rice and Rosengren), that uses Rice’s path independent J-integral, is tried to formulate the stress distribution around the crack tip. In HRR approach, the Ramberg-Osgood model for the stress-strain relation of power-law hardening materials is used to represent the elastic-plastic behavior. Although it is recoverable, the inelastic portion of the deformation in martensitic transformation (up to the end of transformation) resembles to that of plastic deformation. To determine the constants of the Ramberg-Osgood equation, the material’s response is simulated in ABAQUS using a UMAT based on ZM (Zaki-Moumni) thermo-mechanically coupled model, and the stress-strain curve of the material is plotted. An edge cracked shape memory alloy (Nitinol) plate is loaded quasi-statically under mode I and modeled using ABAQUS; the opening stress values ahead of the cracked tip are calculated. The stresses are also evaluated using the asymptotic equations of both LEFM and HRR. The results show that in the transformation zone around the crack tip, the stress values are much better represented when the HRR singularity is used although the J-integral does not show path independent behavior. For the nodes very close to the crack tip, the HRR singularity is not valid due to the non-proportional loading effect and high-stress values that go beyond the transformation finish stress.

Keywords: crack, HRR singularity, shape memory alloys, stress distribution

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Authors: Farhad Imanshoar

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The regime or equilibrium geometry of alluvial rivers remains a topic of fundamental scientific and engineering interest. There are several approaches to analyze the problem, namely: empirical formulas, semi-theoretical methods and rational (extreme) procedures. However, none of them is widely accepted at present, due to lack of knowledge of some physical processes associated with channel formation and the simplification hypotheses imposed in order to reduce the high quantity of involved variables. The study presented in this paper shows a new approach to estimate stable width and depth of sand-bed rivers by using developed stream power equation (DSPE). At first, a new procedure based on theoretical analysis and by considering DSPE and ultimate sediment concentration were developed. Then, experimental data for regime condition in sand-bed rivers (flow depth, flow width, sediment feed rate for several cases) were gathered. Finally, the results of this research (regime equations) are compared with the field data and other regime equations. A good agreement was observed between the field data and the values resulted from developed regime equation.

Keywords: regime equations, developed stream power equation, sand-bed rivers, semi-theoretical methods

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Authors: Shai Sarussi

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Let S be an integral domain which is not a field, let F be its field of fractions, and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R ∩ F = S and F R = A. A topological space whose set of open sets is closed under arbitrary intersections is called an Alexandroff space. Inspired by the well-known Zariski-Riemann space and the Zariski topology on the set of prime ideals of a commutative ring, we define a topology on the set of all S-nice subalgebras of A. Consequently, we get an interplay between Algebra and topology, that gives us a better understanding of the S-nice subalgebras of A. It is shown that every irreducible subset of S-nice subalgebras of A has a supremum; and a characterization of the irreducible components is given, in terms of maximal S-nice subalgebras of A.

Keywords: Alexandroff topology, integral domains, Zariski-Riemann space, S-nice subalgebras

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Authors: Abdulrahman Abdulrahman

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When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: S. Houcine Habib, B. Elkhalil Hachi, Mohamed Guesmi, Mohamed Haboussi

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In this paper, dynamic fracture behaviors of cracked orthotropic structure are modeled using extended finite element method (X-FEM). In this approach, the finite element method model is first created and then enriched by special orthotropic crack tip enrichments and Heaviside functions in the framework of partition of unity. The mixed mode stress intensity factor (SIF) is computed using the interaction integral technique based on J-integral in order to predict cracking behavior of the structure. The developments of these procedures are programmed and introduced in a self-software platform code. To assess the accuracy of the developed code, results obtained by the proposed method are compared with those of literature.

Keywords: X-FEM, composites, stress intensity factor, crack, dynamic orthotropic behavior

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Authors: Nana Adjoah Mbroh, Suares Clovis Oukouomi Noutchie

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Singularly perturbed problems are parameter dependent problems, and they play major roles in the modelling of real-life situational problems in applied sciences. Thus, designing efficient numerical schemes to solve these problems is of much interest since the exact solutions of such problems may not even exist. Generally, singularly perturbed problems are identified by a small parameter multiplying at least the highest derivative in the equation. The presence of this parameter causes the solution of these problems to be characterized by rapid oscillations. This unique feature renders classical numerical schemes inefficient since they are unable to capture the behaviour of the exact solution in the part of the domain where the rapid oscillations are present. In this paper, a numerical scheme is proposed to solve a singularly perturbed Volterra Integro-differential equation. The scheme is based on the midpoint rule and employs the non-standard finite difference scheme to solve the differential part whilst the composite trapezoidal rule is used for the integral part. A fully fledged error estimate is performed, and Richardson extrapolation is applied to accelerate the convergence of the scheme. Numerical simulations are conducted to confirm the theoretical findings before and after extrapolation.

Keywords: midpoint rule, non-standard finite difference schemes, Richardson extrapolation, singularly perturbed problems, trapezoidal rule, uniform convergence

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Authors: Hebert Montegranario, Mauricio Londoño

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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

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Authors: Shai Sarussi

Abstract:

Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: integral domains, Alexandroff topology, prime spectrum of a ring, valuation domains

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Authors: Priyanka Ghosh, Priti Kumar Roy

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Every year a considerable number of people die due to methyl alcohol poisoning, in which most of them die even before proper treatment. This work gives a simple and cheap first aid to those affected individuals by the administration of activated charcoal. In this article, we emphasise on the adsorption capability of activated charcoal for the treatment of poisoning and use an impulsive differential equation to study the effect of activated charcoal during adsorption. We also investigate the effects of various parameters on the adsorption which are incorporated in the model system.

Keywords: activated charcoal, adsorption, impulsive differential equation, methanol poisoning

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Authors: Ritu Rani

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In this paper, we apply minimalistically upheld linear semi-orthogonal B-spline wavelets, exceptionally developed for the limited interim to rough the obscure function present in the integral equations. Semi-orthogonal wavelets utilizing B-spline uniquely developed for the limited interim and these wavelets can be spoken to in a shut frame. This gives a minimized help. Semi-orthogonal wavelets frame the premise in the space L²(R). Utilizing this premise, an arbitrary function in L²(R) can be communicated as the wavelet arrangement. For the limited interim, the wavelet arrangement cannot be totally introduced by utilizing this premise. This is on the grounds that backings of some premise are truncated at the left or right end purposes of the interim. Subsequently, an uncommon premise must be brought into the wavelet development on the limited interim. These functions are alluded to as the limit scaling functions and limit wavelet functions. B-spline wavelet method has been connected to fathom linear and nonlinear integral equations and their systems. The above method diminishes the integral equations to systems of algebraic equations and afterward these systems can be illuminated by any standard numerical methods. Here, we have connected Newton's method with suitable starting speculation for solving these systems.

Keywords: semi-orthogonal, wavelet arrangement, integral equations, wavelet development

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará

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Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

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Authors: Yang Zhong, Meijie Xu

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The explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate with four clamped edges are presented by the double finite cosine integral transform method. In the analysis procedure, the classical orthotropic rectangular thin plate is considered. Because only are the basic dynamic elasticity equations of the orthotropic thin plate adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by this paper is reasonable and theoretical. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.

Keywords: rectangular orthotropic plate, four clamped edges, natural frequencies and mode shapes, finite integral transform

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Authors: Seyed Sadegh Naseralavi

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This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.

Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation

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Authors: A. Benbouali, H. Saidi, A. Derrouazin, T. Bessaad

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Aerial robotics is a very exciting research field dealing with a variety of subjects, including the attitude control. This paper deals with the control of a four rotor vertical take-off and landing (VTOL) Unmanned Aerial Vehicle. The paper presents a mathematical model based on the approach of Lagrange for the flight control of an autonomous quad-rotor. It also describes the controller architecture which is based on PID regulators. The control method has been simulated in closed loop in different situations. All the calculation stages and the simulation results have been detailed.

Keywords: quad-rotor, lagrange approach, proportional integral derivate (PID) controller, Matlab/Simulink

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Authors: Anand Kishore Kola, G. Uday Bhaskar Babu, Kotturi Ajay Kumar

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The modern dynamic systems used in industries are complex in nature and hence the fractional order controllers have been contemplated as a fresh approach to control system design that takes the complexity into account. Traditional integer order controllers use integer derivatives and integrals to control systems, whereas fractional order controllers use fractional derivatives and integrals to regulate memory and non-local behavior. This study provides a method based on the maximumsensitivity (Ms) methodology to discover all resilient fractional filter Internal Model Control - proportional integral derivative (IMC-PID) controllers that stabilize the closed-loop system and deliver the highest performance for a time delay system with a Smith predictor configuration. Additionally, it helps to enhance the range of PID controllers that are used to stabilize the system. This study also evaluates the effectiveness of the suggested controller approach for minimum phase system in comparison to those currently in use which are based on Integral of Absolute Error (IAE) and Total Variation (TV).

Keywords: modern dynamic systems, fractional order controllers, maximum-sensitivity, IMC-PID controllers, Smith predictor, IAE and TV

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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Authors: Rajesh Chakraborty, Dibyendu Das, Rabindra Nath Barman, Uttam Kumar Mandal

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In the present study, the objective is to find out the most effective zone causing soil erosion in the Gumati river basin located in the state of Tripura, a north eastern state of India using analytical hierarchy process (AHP) and multi-objective optimization on the basis of ratio analysis (MOORA).The watershed is segmented into 20 zones based on Area. The watershed is considered by pointing the maximum elevation from sea lever from Google earth. The soil erosion is determined using the universal soil loss equation. The different independent variables of soil loss equation bear different weightage for different soil zones. And therefore, to find the weightage factor for all the variables of soil loss equation like rainfall runoff erosivity index, soil erodibility factor etc, analytical hierarchy process (AHP) is used. And thereafter, multi-objective optimization on the basis of ratio analysis (MOORA) approach is used to select the most effective zone causing soil erosion. The MCDM technique concludes that the maximum soil erosion is occurring in the zone 14.

Keywords: soil erosion, analytic hierarchy process (AHP), multi criteria decision making (MCDM), universal soil loss equation (USLE), multi-objective optimization on the basis of ratio analysis (MOORA)

Procedia PDF Downloads 510