A NEW NUMERICAL METHOD TO SOLVE NONLINEAR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS-Reference-Cited by-同舟云学术

A NEW NUMERICAL METHOD TO SOLVE NONLINEAR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

Published:2021-09-10 Issue:3 Volume:26 Page:469-478
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
language:
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Author:

Hou Jinjiao¹^ORCID,Niu Jing¹^ORCID,Ngolo Welreach²

Affiliation:

1. School of Mathematics and Sciences, Harbin Normal University, 150025 Harbin, China

2. College of Science, Zhejiang University of Technology, 310014 Hangzhou, China

Abstract

In this paper, a new method combining the simplified reproducing kernel method (SRKM) and the homotopy perturbation method (HPM) to solve the nonlinear Volterra-Fredholm integro-differential equations (V-FIDE) is proposed. Firstly the HPM can convert nonlinear problems into linear problems. After that we use the SRKM to solve the linear problems. Secondly, we prove the uniform convergence of the approximate solution. Finally, some numerical calculations are proposed to verify the effectiveness of the approach.

Publisher

Vilnius Gediminas Technical University

Subject

Modelling and Simulation,Analysis

Reference18 articles.

1. The Barycentric Rational Difference-Quadrature Scheme for Systems of Volterra Integro-differential Equations

2. NEW DIRECT METHOD TO SOLVE NONLINEAR VOLTERRA-FREDHOLM INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS USING OPERATIONAL MATRIX WITH BLOCK-PULSE FUNCTIONS

3. Numerical solution of nonlinear Volterra–Fredholm integro-differential equations via direct method using triangular functions

4. Laplace Discrete Adomian Decomposition Method for Solving Nonlinear Integro Differential Equations

5. He’s homotopy perturbation method: A strongly promising method for solving non-linear systems of the mixed Volterra–Fredholm integral equations

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