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

Li Huang; Yu Lin Zhao; Liang Tang

doi:10.4028/www.scientific.net/AMM.220-223.2129

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 220-223Solving the Volterra Integral Equations with...

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

Abstract:

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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Periodical:

Applied Mechanics and Materials (Volumes 220-223)

Pages:

2129-2132

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.220-223.2129

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Online since:

November 2012

Authors:

Li Huang, Yu Lin Zhao, Liang Tang

Keywords:

Approximate Solution, Integration Method, Taylor Expansion, Volterra Integral Equations, Weakly Singular Kernel

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