Numerical solution of the nonlinear Fredholm integral equations by positive definite functions

Alipanah, Amjad; Dehghan, Mehdi

doi:10.1016/j.amc.2007.02.063

Cited by 45 publications

(26 citation statements)

References 11 publications

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“…Also partial integro-differential equation is a good model for viscoelasticity (see for example [10] and the references therein). The interested reader can see [4,[11][12][13][14][15][16][17] for more research works on the numerical solution of integral equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients

Saadatmandi

Dehghan

2010

Computers & Mathematics with Applications

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a b s t r a c tThe main aim of this paper is to apply the Legendre polynomials for the solution of the linear Fredholm integro-differential-difference equation of high order. This equation is usually difficult to solve analytically. Our approach consists of reducing the problem to a set of linear equations by expanding the approximate solution in terms of shifted Legendre polynomials with unknown coefficients. The operational matrices of delay and derivative together with the tau method are then utilized to evaluate the unknown coefficients of shifted Legendre polynomials. Illustrative examples are included to demonstrate the validity and applicability of the presented technique and a comparison is made with existing results.

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Section: Introductionmentioning

confidence: 99%

Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients

Saadatmandi

Dehghan

2010

Computers & Mathematics with Applications

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“…The main advantage of radial basis functions methods are the meshless characteristic of them. These methods have recently received a great deal of attention from researchers [25], [26], [27], [28], [29], [30], [31], [32]. Recently, RBFs methods were extended to solve various ordinary and partial differential equations including the high order ordinary differential equations [33], secondorder parabolic equation with nonlocal boundary conditions [34], the nonlinear Klein-Gordon equation [29], regularized long wave (RLW) equation [35], Hirota-Satsuma coupled KdV equations [36], a system of nonlinear integral equations [37], Second-order hyperbolic telegraph equation [38], the solution of 2D biharmonic equations [39], the case of heat transfer equations [40], a class of astrophysics problems [41] and so on.…”

Section: Introductionmentioning

confidence: 99%

An RBF Solution to a Stagnation Point Flow Towards a Stretching Surface with Heat Generation

Kazem

Sanaeikia

Ahmadvand

et al. 2011

2011 14th IEEE International Conference on Computational Science and Engineering

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In this paper, we propose radial basis function (RBF) to solve nonlinear momentum and energy equations obtained from modeling steady laminar flow through a porous medium of an incompressible viscous conducting fluid impinging on a permeable stretching surface with heat generation. This flow impinges normal to a plane wall with heat transfer. Our reports consist of the effect of the porosity of the medium, the surface stretching velocity, and the heat generation/absorption coefficient on both the flow and heat transfer. A simple solution by using collocation points over the almost whole domain [0, ∞) is obtaind. We apply this method through the definite integration process and satisfy the infinity boundary condition by using Gaussian RBF.

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“…The properties of these multiwavelets are then utilized to evaluate the unknown coefficients. We refer the interested reader to [32][33][34][35][36][37][38][39][40][41][42][43][44] for some basic ideas on numerical solution of integral equations. Also the reader can see [45,46] for applications of the partial integro-differential equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for the weakly singular Fredholm integro-differential equations using Legendre multiwavelets

Lakestani

Saray

Dehghan

2011

Journal of Computational and Applied Mathematics

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a b s t r a c tAn effective method based upon Legendre multiwavelets is proposed for the solution of Fredholm weakly singular integro-differential equations. The properties of Legendre multiwavelets are first given and their operational matrices of integral are constructed. These wavelets are utilized to reduce the solution of the given integro-differential equation to the solution of a sparse linear system of algebraic equations. In order to save memory requirement and computational time, a threshold procedure is applied to obtain the solution to this system of algebraic equations. Through numerical examples, performance of the present method is investigated concerning the convergence and the sparseness of the resulted matrix equation.

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Numerical solution of the nonlinear Fredholm integral equations by positive definite functions

Cited by 45 publications

References 11 publications

Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients

Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients

An RBF Solution to a Stagnation Point Flow Towards a Stretching Surface with Heat Generation

Numerical solution for the weakly singular Fredholm integro-differential equations using Legendre multiwavelets

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