On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials

AbstractThis paper is concerned with the numerical solution for a class of weakly singular Fredholm integral equations of the second kind. The Taylor series of the unknown function, is used to remove the singularity and the truncated Taylor series to second order of k(x, y) about the point (x

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Regularization and Fourier Series for Fredholm Integral Equations of the Second Kind with a Weakly Singular Kernel

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2017.1364753 ◽

2017 ◽

Vol 39 (1) ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Hamza Guebbai

Keyword(s):

Fourier Series ◽

Integral Equations ◽

Singular Kernel ◽

Fredholm Integral Equations ◽

Weakly Singular Kernel ◽

Weakly Singular

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Legendre multi-Galerkin methods for Fredholm integral equations with weakly singular kernel and the corresponding eigenvalue problem

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.07.010 ◽

2019 ◽

Vol 346 ◽

pp. 224-236 ◽

Cited By ~ 4

Author(s):

Bijaya Laxmi Panigrahi ◽

Moumita Mandal ◽

Gnaneshwar Nelakanti

Keyword(s):

Eigenvalue Problem ◽

Integral Equations ◽

Singular Kernel ◽

Fredholm Integral Equations ◽

Galerkin Methods ◽

Weakly Singular Kernel ◽

Weakly Singular

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Numerical solution of Volterra integral equations with weakly singular kernel based on the DE-sinc method

Japan Journal of Industrial and Applied Mathematics ◽

10.1007/bf03167518 ◽

2008 ◽

Vol 25 (2) ◽

pp. 165-183 ◽

Cited By ~ 7

Author(s):

Masatake Mori ◽

Ahniyaz Nurmuhammad ◽

Takefumi Murai

Keyword(s):

Numerical Solution ◽

Integral Equations ◽

Volterra Integral Equations ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Sinc Method ◽

Weakly Singular

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Numerical solutions for Fredholm integral equations of the second kind with weakly singular kernel using spectral collocation method

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.12.035 ◽

2019 ◽

Vol 349 ◽

pp. 314-324 ◽

Cited By ~ 2

Author(s):

Yin Yang ◽

Zhuyan Tang ◽

Yunqing Huang

Keyword(s):

Integral Equations ◽

Collocation Method ◽

Numerical Solutions ◽

Spectral Collocation Method ◽

Singular Kernel ◽

Fredholm Integral Equations ◽

Spectral Collocation ◽

Weakly Singular Kernel ◽

Weakly Singular

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Solving the Volterra Integral Equations with Weakly Singular Kernel by Taylor Expansion Methods

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.220-223.2129 ◽

2012 ◽

Vol 220-223 ◽

pp. 2129-2132

Author(s):

Li Huang ◽

Yu Lin Zhao ◽

Liang Tang

Keyword(s):

Integral Equation ◽

Integral Equations ◽

Unknown Function ◽

Taylor Expansion ◽

Closed Form Solution ◽

Form Solution ◽

Volterra Integral Equations ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Weakly Singular

In this paper, we propose a Taylor expansion method for solving (approximately) linear Volterra integral equations with weakly singular kernel. By means of the nth-order Taylor expansion of the unknown function at an arbitrary point, the Volterra integral equation can be converted approximately to a system of equations for the unknown function itself and its n derivatives. This method gives a simple and closed form solution for the integral equation. In addition, some illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method.

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