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Research Article | Open Access

A high order approach for nonlinear Volterra-Hammerstein integral equations

Jian Zhang, Jinjiao Hou, Jing Niu( ), Ruifeng Xie( ), Xuefei Dai
Harbin Normal University, Harbin 150025, China
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Abstract

Here a scheme for solving the nonlinear integral equation of Volterra-Hammerstein type is given. We combine the related theories of homotopy perturbation method (HPM) with the simplified reproducing kernel method (SRKM). The nonlinear system can be transformed into linear equations by utilizing HPM. Based on the SRKM, we can solve these linear equations. Furthermore, we discuss convergence and error analysis of the HPM-SRKM. Finally, the feasibility of this method is verified by numerical examples.

Keywords

reproducing kernel methodhomotopy perturbation methodVolterra-Hammerstein integral equations
CLC number: 45G10, 45J05

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 1460-1469
DOI: 10.3934/math.2022086

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Cite this article:
Zhang J, Hou J, Niu J, et al. A high order approach for nonlinear Volterra-Hammerstein integral equations. AIMS Mathematics, 2022, 7(1): 1460-1469. https://doi.org/10.3934/math.2022086

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Received: 02 September 2021
Accepted: 20 October 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)