Computational Methods for Linear Integral Equations

Kythe, Prem K.; Puri, P.

doi:10.1007/978-1-4612-0101-4

Cited by 168 publications

(108 citation statements)

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“…In this section we state some definitions and theorems [11,20] that will be used later in our work. Definition 1.…”

Section: Complex B -Splinesmentioning

confidence: 99%

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Complex B-spline Collocation method for solving weakly singular Volterra integral equations of the second kind

Jafari¹,

Ramezani²,

Johnston³

et al. 2015

Miskolc Math Notes

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Abstract. In this paper we propose a new collocation type method for solving Volterra integral equations of the second kind with weakly singular kernels. In this method we use the complex Bspline basics in collocation method for solving Volterra integral. We compare the results obtained by this method with exact solution. A few numerical examples are presented to demonstrate the effectiveness of the proposed method.

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“…In this section we state some definitions and theorems [11,20] that will be used later in our work. Definition 1.…”

Section: Complex B -Splinesmentioning

confidence: 99%

“…In most of the cases, it is difficult to obtain analytical solution of integral equations, therefore many numerical methods such as collocation method with different basics [2,19,20], orthogonal bases and wavelets [17,21], Galerkin methods have been developed to solve equation (1.1) [4][5][6]14].…”

Section: Introductionmentioning

confidence: 99%

Complex B-spline Collocation method for solving weakly singular Volterra integral equations of the second kind

Jafari¹,

Ramezani²,

Johnston³

et al. 2015

Miskolc Math Notes

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show abstract

“…All authors read and approved the final manuscript. 1 Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou, 425100, P.R. China.…”

Section: Competing Interestsmentioning

confidence: 99%

Fast multipole method for singular integral equations of second kind

Xiang

2015

Adv Differ Equ

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This paper explores the numerical methods for a singular integral equation (SIE), which arise in the study of various problems of mathematical physics and engineering. The idea behind the boundary element method (BEM) is used to discretize the SIE. The fast multipole method (FMM), which is a very efficient and popular algorithm for the rapid solution of boundary value problems, is used to accelerate the BEM solutions of SIE. The effectiveness and accuracy of the proposed method are tested by numerical examples.

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“…For systems of such equations, various techniques such as extrapolation method, Galerkin discretization, collocation methods, and quadrature, iterative, spline, orthogonal polynomial, and multiple grid methods have been proposed to determine desired solutions (see, e.g., [6][7][8][9] and the references quoted there). These methods include approximate analytical and numerical approaches.…”

Section: Introductionmentioning

confidence: 99%

New Operational Matrix of Integrations and Coupled System of Fredholm Integral Equations

Khalil

Khan

2014

Chinese Journal of Mathematics

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We study Legendre polynomials and develop new operational matrix of integration. Based on the operational matrix, we develop a new method to solve a coupled system of Fredholm integral equations of the form ( ) + 11 ∫ . The method reduces the coupled system to a system of easily solvable algebraic equations without discretizing the original system. As an application, we provide examples and numerical simulations demonstrating that the results obtained using the new technique match very well with the exact solutions of the problems. To show the efficiency of the method, we compare our results with some of the results already studied with other available methods in the literature.

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Computational Methods for Linear Integral Equations

Cited by 168 publications

References 0 publications

Complex B-spline Collocation method for solving weakly singular Volterra integral equations of the second kind

Complex B-spline Collocation method for solving weakly singular Volterra integral equations of the second kind

Fast multipole method for singular integral equations of second kind

New Operational Matrix of Integrations and Coupled System of Fredholm Integral Equations

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