An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential Equations
We propose and apply coupling of the variational iteration method (VIM) and homotopy perturbation method (HPM) to solve nonlinear mixed Volterra-Fredholm integrodifferential equations (VFIDE). In this approach, we use a new formula called variational homotopy perturbation method (VHPM) and variation...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/9385040 |
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| author | F. A. Hendi M. M. Al-Qarni |
| author_facet | F. A. Hendi M. M. Al-Qarni |
| author_sort | F. A. Hendi |
| collection | DOAJ |
| description | We propose and apply coupling of the variational iteration method (VIM) and homotopy perturbation method (HPM) to solve nonlinear mixed Volterra-Fredholm integrodifferential equations (VFIDE). In this approach, we use a new formula called variational homotopy perturbation method (VHPM) and variational accelerated homotopy perturbation method (VAHPM). This approach is based on the form of He’s polynomials and on a new form of He’s polynomials. We discuss the convergence of the technique. Some numerical examples are introduced to verify the efficiency of this technique. |
| format | Article |
| id | doaj-art-aafce8832e124e18b6d3b961651fa322 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-aafce8832e124e18b6d3b961651fa3222025-02-03T05:45:40ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/93850409385040An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential EquationsF. A. Hendi0M. M. Al-Qarni1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi ArabiaWe propose and apply coupling of the variational iteration method (VIM) and homotopy perturbation method (HPM) to solve nonlinear mixed Volterra-Fredholm integrodifferential equations (VFIDE). In this approach, we use a new formula called variational homotopy perturbation method (VHPM) and variational accelerated homotopy perturbation method (VAHPM). This approach is based on the form of He’s polynomials and on a new form of He’s polynomials. We discuss the convergence of the technique. Some numerical examples are introduced to verify the efficiency of this technique.http://dx.doi.org/10.1155/2017/9385040 |
| spellingShingle | F. A. Hendi M. M. Al-Qarni An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential Equations Advances in Mathematical Physics |
| title | An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential Equations |
| title_full | An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential Equations |
| title_fullStr | An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential Equations |
| title_full_unstemmed | An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential Equations |
| title_short | An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential Equations |
| title_sort | accelerated homotopy perturbation method for solving nonlinear two dimensional volterra fredholm integrodifferential equations |
| url | http://dx.doi.org/10.1155/2017/9385040 |
| work_keys_str_mv | AT fahendi anacceleratedhomotopyperturbationmethodforsolvingnonlineartwodimensionalvolterrafredholmintegrodifferentialequations AT mmalqarni anacceleratedhomotopyperturbationmethodforsolvingnonlineartwodimensionalvolterrafredholmintegrodifferentialequations AT fahendi acceleratedhomotopyperturbationmethodforsolvingnonlineartwodimensionalvolterrafredholmintegrodifferentialequations AT mmalqarni acceleratedhomotopyperturbationmethodforsolvingnonlineartwodimensionalvolterrafredholmintegrodifferentialequations |