Efficient Numerical Algorithm for the Solution of Nonlinear Two‐Dimensional Volterra Integral Equation Arising from Torsion Problem

A. M. Al-Bugami

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: In this article, an effective method is given to solve nonlinear two‐dimensional Volterra integral equations of the second kind, which is arising from torsion problem for a long bar that consists of the nonlinear viscoelastic material type with a fixed elliptical cross section. First, the existence of a unique solution of this problem is discussed, and then, we find the solution of a nonlinear two‐dimensional Volterra integral equation (NT‐DVIE) using block‐by‐block method (B‐by‐BM) and degenerate kernel method (DKM). Numerical examples are presented, and their results are compared with the analytical solution to demonstrate the validity and applicability of the method.

Date: 2021
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https://doi.org/10.1155/2021/6559694

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:6559694

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