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A new numerical method to solve nonlinear Volterra-Fredholm integro-differential equations

    Jinjiao Hou   Affiliation
    ; Jing Niu   Affiliation
    ; Welreach Ngolo Affiliation

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.

Keyword : nonlinear Volterra-Fredholm integro-differential equations, simplified reproducing kernel method, homotopy perturbation method

How to Cite
Hou, J., Niu, J., & Ngolo, W. (2021). A new numerical method to solve nonlinear Volterra-Fredholm integro-differential equations. Mathematical Modelling and Analysis, 26(3), 469-478. https://doi.org/10.3846/mma.2021.12923
Published in Issue
Sep 9, 2021
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