Modified Product Block By Block For The Second Kind Volterra Integral Equations With Singular Kernel

G. Attia

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Research Article

7 (

); 13-20

Modified Product Block By Block For The Second Kind Volterra Integral Equations With Singular Kernel

G. Attia

Received: 2020-02-25, Accepted: 2020-02-25, Published: 2014-01-01

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This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-Share Alike 4.0 License, which allows others to remix, transform, and build upon the work non-commercially, as long as the author is credited and the new creations are licensed under the identical terms.

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This article was originally published by Qassim University and was migrated to Scientific Scholar after the change of Publisher.

Abstract

The block-by -block method is a good self-starting method for solving Volterra Integral equations of the second kind with continuous kernel. In this paper two modifications are suggested to develop block by block method to solve Volterra integral equations with weakly singular kernels. The idea of the product technique with higher order is used for block-by block method, which is the first modification, while the second modification is using the method on the graded nodes. Implementation and testing of the considered algorithms have been done. The results showed that this method gives good results compared with others methods on equal spaced nodes.