A high order approach for nonlinear Volterra-Hammerstein integral equations

Jian Zhang; Jinjiao Hou; Jing Niu; Ruifeng Xie; Xuefei Dai; Jian Zhang; Jinjiao Hou; Jing Niu; Ruifeng Xie; Xuefei Dai

doi:10.3934/math.2022086

AIMS Mathematics

2022, Volume 7, Issue 1: 1460-1469. doi: 10.3934/math.2022086

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A high order approach for nonlinear Volterra-Hammerstein integral equations

Harbin Normal University, Harbin 150025, China

Received: 02 September 2021 Accepted: 20 October 2021 Published: 26 October 2021
MSC : 45G10, 45J05

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.
- reproducing kernel method,
- homotopy perturbation method,
- Volterra-Hammerstein integral equations
Citation: Jian Zhang, Jinjiao Hou, Jing Niu, Ruifeng Xie, Xuefei Dai. A high order approach for nonlinear Volterra-Hammerstein integral equations[J]. AIMS Mathematics, 2022, 7(1): 1460-1469. doi: 10.3934/math.2022086

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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.

References

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