Higher Order Product Block by Block Method for Nonlinear Volterra Integral Equations of the Second Kind with Weakly Singular Kernel

G. Attia; H. Nour; G. El-Baghdady

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Research Article

8 (

); 15-27

Higher Order Product Block by Block Method for Nonlinear Volterra Integral Equations of the Second Kind with Weakly Singular Kernel

G. Attia, H. Nour, G. El-Baghdady

Received: 2020-02-26, Accepted: 2020-02-26, Published: 2015-01-01

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

Abstract

In this paper product block technique is modified to solve nonlinear Volterra integral equations of the second kind when the kernel contains mild singularity. The product block by block method is modified by using two suggestions. Firstly we use Bool's quadrature rule which has high order of convergence. Secondly the Bool's block is adapted to use on graded nodes. To illustrate the effectiveness of the developed method a number of numerical examples are presented and a comparison with Simpson's product block by block is made.