Solving two-dimensional integral equations

Bazrafshan, Foroud; Mahbobi, A.H.; Neyrameh, A.; Sousaraie, A.; Ebrahimi, Morteza

doi:10.1016/j.jksus.2010.06.017

Cited by 7 publications

(8 citation statements)

References 9 publications

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“…For speed up the calculations Liao [33] suggested to replace the integral in formula (12) by its approximate value obtained by applying the quadrature rules. In examples presented by Liao the received optimal values of the convergence control parameter differ not much from the values obtained by applying formula (12).…”

Section: Homotopy Analysis Methodsmentioning

confidence: 99%

“…In examples presented by Liao the received optimal values of the convergence control parameter differ not much from the values obtained by applying formula (12). The residual error method for obtaining the convergence control parameter (h), shown in (12), has been applied recently to a number of problems for nonlinear ODEs and PDEs [3,7,11,19,21,32,39,[49][50][51].…”

Section: Homotopy Analysis Methodsmentioning

confidence: 99%

“…In papers [40,42] the examples of using the method for solving the system of integral equations are presented. Whereas the examples of applying the method for solving the twodimensional integral equations can be found in works [5,12]. Next, in papers [13,36] the possibility of using the method for solving the fuzzy integral equations is shown.…”

Section: Introductionmentioning

confidence: 99%

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Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind

et al. 2013

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The paper presents an application of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind. In this method a series is created, sum of which (if the series is convergent) gives the solution of discussed equation. Conditions ensuring convergence of this series are presented in the paper. Error of approximate solution, obtained by considering only partial sum of the series, is also estimated. Examples illustrating usage of the investigated method are presented as well, including the example having practical application for calculating the charge in supply circuit of flash lamps used in cameras.

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Section: Homotopy Analysis Methodsmentioning

confidence: 99%

Section: Homotopy Analysis Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind

et al. 2013

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“…Research on the two-dimensional case has been getting more attention recently [8][9][10][11][12][13][14][15]. The main goal in this work is to extend the regularization-homotopy method introduced in [7] for one dimensional Fredholm integral equations of the first kind to two-dimensional Fredholm integral equations of the first kind.…”

Section: Introductionmentioning

confidence: 99%

The Regularization-Homotopy Method for the Two-Dimensional Fredholm Integral Equations of the First Kind

Altürk

2016

MCA

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Abstract:In this work, we consider two-dimensional linear and nonlinear Fredholm integral equations of the first kind. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method is used to find a solution to the equation. The application of this method is based upon converting the first kind of equation to the second kind by applying the regularization method. Then the homotopy perturbation method is employed to the resulting second kind of equation to obtain a solution. A few examples including linear and nonlinear equations are provided to show the validity and applicability of this approach.

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“…In [1], Bazrafshan et al applied the homotopy analysis method to solve two-dimensional integral equations. In [2], Maleknejad et al presented a numerical method to solve two-dimensional integral equations called triangular functions method.…”

Section: Introductionmentioning

confidence: 99%

Equivalence between homotopy perturbation method and Adomian decomposition method in solving two dimensional linear Fredholm integral equations

Almousa

Ismail

2014

AIP Conference Proceedings

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Articles you may be interested inThe solution of high dimensional Fredholm integral equations using homotopy perturbation method AIP Conf. Proc. 1635, 52 (2014); 10.1063/1.4903562 Numerical solution of Fredholm-Hammerstein integral equations by using optimal homotopy asymptotic method and homotopy perturbation method AIP Conf. Proc. 1605, 90 (2014); 10.1063/1.4887570Identifying an unknown function in a parabolic equation by homotopy analysis method and comparison with the adomian decomposition method AIP Conf.Abstract. In this study, we present comparison between the ADM and the HPM for solving two-dimensional linear Fredholm integral equations. The analytical results revealed that the two methods give same solution for solving twodimensional linear Fredholm integral equations. Moreover, these methods are powerful and easy to implement.

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Solving two-dimensional integral equations

Cited by 7 publications

References 9 publications

Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind

Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind

The Regularization-Homotopy Method for the Two-Dimensional Fredholm Integral Equations of the First Kind

Equivalence between homotopy perturbation method and Adomian decomposition method in solving two dimensional linear Fredholm integral equations

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