Legendre-collocation method to solve the second kind Cauchy integral equations

Document Type : Research Article

Authors

1 Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics‎, ‎South Tehran Branch‎, ‎Islamic Azad University‎, ‎Tehran‎, ‎Iran

Abstract

 A numerical solution for the second kind singular integral equations with Cauchy kernel is developed using the collocation method. To achieve this, we approximate the Cauchy integral equation using the collocation method and Legendre orthogonal polynomial expansions. The accuracy of our proposed method is assessed through convergence and error analysis. Finally, several numerical examples are presented to  demonstrate the high efficiency of the method.

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Journal of Mathematical Modeling
Volume 13, Issue 1
March 2025
Pages 209-218

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