Numerical solution of the two-dimensional Fredholm integral equations using Gaussian radial basis function

Alipanah, Amjad; Esmaeili, Shahrokh

doi:10.1016/j.cam.2009.11.053

Cited by 69 publications

(43 citation statements)

References 14 publications

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“…Consider the following linear two-dimensional Fredholm integral equation of the second kind with a non-degenerate kernel [2,6] …”

Section: Test Examplementioning

confidence: 99%

The relationship of degenerate kernel and projection methods on Fredholm integral equations of the second kind

Molabahrami¹

2017

Communications in Numerical Analysis

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In this paper, we show that the degenerate kernel method for some cases, on the condition that the source function is approximated by the same way of producing degenerate kernel, becomes as a projection method. We consider two ways, including Lagrange interpolation and best approximation methods, of producing degenerate kernel approximations of more general Fredholm integral equation of the second kind. For these two ways, we show that the degenerate kernel method becomes as a Lagrange-collocation method and Galerkin method respectively.

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“…Consider the following linear two-dimensional Fredholm integral equation of the second kind with a non-degenerate kernel [2,6] …”

Section: Test Examplementioning

confidence: 99%

The relationship of degenerate kernel and projection methods on Fredholm integral equations of the second kind

Molabahrami¹

2017

Communications in Numerical Analysis

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“…For example, it is usually required to solve Fredholm integral equations in the calculation of plasma physics (Farengo et al, 1983). There are many works on developing and analyzing numerical methods for solving Fredholm integral equations of the second kind (see Alipanah and Esmaeili, 2009;Alpert et al, 1993;Anselon, 1971;Atkinson, 1976Atkinson, , 1997Baker, 1977;Delves and Mohamed, 1985). The subject of the presented paper is applying the 2D-TFs method for solving two-dimensional linear Fredholm integral equations.…”

Section: Introductionmentioning

confidence: 98%

Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions

Mirzaee

Piroozfar

2010

Journal of King Saud University - Science

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In this paper, we will give some results for developing the two-dimensional triangular orthogonal functions (2D-TFs) for numerical solution of the linear two-dimensional Fredholm integral equations of the second kind. The product of 2D-TFs and some formulas for calculating definite integral of them are derived and utilized to reduce the solution of two-dimensional Fredholm integral equation to the solution of algebraic equations. Also a theorem is proved for convergence analysis. Numerical examples are presented and results are compared with analytical solution to demonstrate the validity and applicability the method.

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“…The literature on the numerical solution methods of such equations is fairly extensive [2][3][4][5][6][7][8][9]. But the analysis of computational methods for two-dimensional integral equations seem to have been discussed in only a few papers [10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Applying the modified block-pulse functions to solve the three-dimensional Volterra–Fredholm integral equations

Mirzaee

Hadadiyan

2015

Applied Mathematics and Computation

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Numerical solution of the two-dimensional Fredholm integral equations using Gaussian radial basis function

Cited by 69 publications

References 14 publications

The relationship of degenerate kernel and projection methods on Fredholm integral equations of the second kind

The relationship of degenerate kernel and projection methods on Fredholm integral equations of the second kind

Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions

Applying the modified block-pulse functions to solve the three-dimensional Volterra–Fredholm integral equations

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