A high order approach for nonlinear Volterra-Hammerstein integral equations-Reference-Cited by-同舟云学术

A high order approach for nonlinear Volterra-Hammerstein integral equations

Published:2021 Issue:1 Volume:7 Page:1460-1469
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference34 articles.

1. A. M. Bica, M. Curila, S. Curila, About a numerical method of successive interpolations for functional Hammerstein integral equations, J. Comput. Appl. Math., 236 (2012), 2005–2024. doi: 10.1016/j.cam.2011.11.010.

2. C. E. Chidume, N. Djitté, An iterative method for solving nonlinear integral equations of Hammerstein type, Appl. Math. Comput., 219 (2013), 5613–5621. doi: 10.1016/j.amc.2012.11.051.

3. A. Karoui, A. Jawahdou, Existence and approximate $L^{p}$ and continuous solutions of nonlinear integral equations of the Hammerstein and Volterra types, Appl. Math. Comput., 216 (2010), 2077–2091. doi: 10.1016/j.amc.2010.03.042.

4. M. Mandal, G. Nelakanti, Legendre spectral Galerkin and multi-Galerkin methods for nonlinear Volterra integral equations of Hammerstein type, J. Anal., 28 (2019), 323–349. doi: 10.1007/s41478-019-00170-8.

5. Y. Ordokhani, M. Razzaghi, Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via a collocation method and rationalized Haar functions, Appl. Math. Lett., 21 (2008), 4–9. doi: 10.1016/j.aml.2007.02.007.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An efficient numerical algorithm for solving nonlinear Volterra integral equations in the reproducing kernel space;Journal of Applied Mathematics and Computing;2023-05-24

2. A broken reproducing kernel method for the multiple interface problems;Computational and Applied Mathematics;2022-07-24

3. Lobatto-reproducing kernel method for solving a linear system of second order boundary value problems;Journal of Applied Mathematics and Computing;2021-12-22