Using the Petrov–Galerkin elements for solving Hammerstein integral equations

Maleknejad, K.; Karami, M.; Rabbani, Mohsen

doi:10.1016/j.amc.2005.02.041

Cited by 14 publications

(10 citation statements)

References 5 publications

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“…Method II (using the shifted Chebyshev polynomials and Galerkin methods with the approach of the equivalent equation). In this approach, first, by using the shifted Chebyshev polynomials, we obtain 13,15,34 u(y) '…”

Section: Algorithmmentioning

confidence: 99%

An efficient algorithmic method to solve Hammerstein integral equations and application to a functional differential equation

Abdolmaleki

Najafi

2017

Advances in Mechanical Engineering

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In this article, we present an efficient method for solving nonlinear Fredholm integral equations of the second kind. The proposed method is based on the Galerkin method and transformations of shifted Chebyshev polynomials. This method is simple and computationally very attractive. Finally, illustrative examples and also the application of the proposed method to solve a functional differential equation are presented to show the validity and applicability of the technique.

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Section: Algorithmmentioning

confidence: 99%

An efficient algorithmic method to solve Hammerstein integral equations and application to a functional differential equation

Abdolmaleki

Najafi

2017

Advances in Mechanical Engineering

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“…For the numerical solution of Fredholm integral equations, Galerkin methods are used in [12-14, 20, 23, 30-32]. Other methods use spline functions and wavelets [30,33,34], product integration [13,35], homotopy analysis techniques [36] homotopy perturbation and Adomian decomposition method [37,38], polynomial interpolation procedures and suboptimal trajectories [25,39], multigrid methods [13,40]. Nystrom techniques are used in [12,13,18,[41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Numerical approach for solving neutral differential equation with deviating argument

Mesgarani

Mollapourasl

Ostadi

2015

Comput. Math. and Math. Phys.

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In this article, numerical solution of a neutral differential equation with deviating argu ment by means of the Sinc scheme and fixed point theorem is considered. Properties of the DE Sinc and SE Sinc quadratures are utilized to reduce the computation of the neutral differential equations to an iterative technique. Then convergence of this technique is discussed by preparing a theorem. To guarantee the analytical results and show the efficiency and accuracy of the present method, some examples are presented.

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“…The collocation techniques are involved in . For the numerical solution of Fredholm integral equations, Galerkin methods are used in . Other methods use spline functions and wavelets , product integration , homotopy analysis techniques homotopy perturbation and Adomian decomposition method , polynomial interpolation procedures and suboptimal trajectories , multigrid methods .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

Maleknejad

Mollapourasl

Mirzaei

2013

Numerical Methods Partial

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In this article, we consider a class of nonlinear functional integral equations which has rather general form and contains a lot of particular cases such as functional equations and nonlinear integral equations of Volterra type. We use a combination of a fixed point method and cubic semiorthogonal B‐spline scaling functions to solve the integral equation numerically. We provide an error analysis for the method which shows that the approximate solution converges to the exact solution. Some numerical results for several test problems are given to confirm the accuracy and the ease of implementation of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 699–722, 2014

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Using the Petrov–Galerkin elements for solving Hammerstein integral equations

Cited by 14 publications

References 5 publications

An efficient algorithmic method to solve Hammerstein integral equations and application to a functional differential equation

An efficient algorithmic method to solve Hammerstein integral equations and application to a functional differential equation

Numerical approach for solving neutral differential equation with deviating argument

Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

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