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

A. M. AlBugami | Zendy

Open Access

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

Author(s) -

A. M. AlBugami

Publication year - 2021

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2021/6559694

Subject(s) - nonlinear system , volterra integral equation , mathematics , integral equation , torsion (gastropod) , degenerate energy levels , mathematical analysis , kernel (algebra) , block (permutation group theory) , numerical analysis , geometry , physics , medicine , surgery , quantum mechanics , combinatorics

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.

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