求解非线性Volterra-Fredholm积分微分方程的一种新的数值方法

IF 1.6 3区数学 Q1 MATHEMATICS

Mathematical Modelling and Analysis Pub Date : 2021-09-10 DOI:10.3846/mma.2021.12923

Jinjiao Hou, J. Niu, Welreach Ngolo

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引用次数: 1

摘要

本文提出了一种结合简化再现核法(SRKM)和同伦摄动法(HPM)求解非线性Volterra-Fredholm积分微分方程(V-FIDE)的新方法。首先，HPM可以将非线性问题转化为线性问题。之后我们使用SRKM来解决线性问题。其次，证明了近似解的一致收敛性。最后，通过数值计算验证了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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