A high order approach for nonlinear Volterra-Hammerstein integral equations
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....
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022086?viewType=HTML |
| _version_ | 1798022173710876672 |
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| author | Jian Zhang Jinjiao Hou Jing Niu Ruifeng Xie Xuefei Dai |
| author_facet | Jian Zhang Jinjiao Hou Jing Niu Ruifeng Xie Xuefei Dai |
| author_sort | Jian Zhang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T17:25:33Z |
| format | Article |
| id | doaj.art-4a630930e2d041538a6b9ba96fdb0eb8 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T17:25:33Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-4a630930e2d041538a6b9ba96fdb0eb82022-12-22T04:12:19ZengAIMS PressAIMS Mathematics2473-69882022-01-01711460146910.3934/math.2022086A high order approach for nonlinear Volterra-Hammerstein integral equationsJian Zhang0Jinjiao Hou1Jing Niu2Ruifeng Xie 3Xuefei Dai4Harbin Normal University, Harbin 150025, ChinaHarbin Normal University, Harbin 150025, ChinaHarbin Normal University, Harbin 150025, ChinaHarbin Normal University, Harbin 150025, ChinaHarbin Normal University, Harbin 150025, ChinaHere 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.https://www.aimspress.com/article/doi/10.3934/math.2022086?viewType=HTMLreproducing kernel methodhomotopy perturbation methodvolterra-hammerstein integral equations |
| spellingShingle | Jian Zhang Jinjiao Hou Jing Niu Ruifeng Xie Xuefei Dai A high order approach for nonlinear Volterra-Hammerstein integral equations AIMS Mathematics reproducing kernel method homotopy perturbation method volterra-hammerstein integral equations |
| title | A high order approach for nonlinear Volterra-Hammerstein integral equations |
| title_full | A high order approach for nonlinear Volterra-Hammerstein integral equations |
| title_fullStr | A high order approach for nonlinear Volterra-Hammerstein integral equations |
| title_full_unstemmed | A high order approach for nonlinear Volterra-Hammerstein integral equations |
| title_short | A high order approach for nonlinear Volterra-Hammerstein integral equations |
| title_sort | high order approach for nonlinear volterra hammerstein integral equations |
| topic | reproducing kernel method homotopy perturbation method volterra-hammerstein integral equations |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022086?viewType=HTML |
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