Modification of Homotopy Perturbation method for addressing systems of PDEs
This work employs a refined variation of the Homotopy Perturbation Method (HPM), termed the Modified Homotopy Perturbation Method (MHPM), designed to obtain accurate solutions for significant systems of partial differential equations (PDEs). By incorporating Laplace transforms and Padé approximants,...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-03-01
|
| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124004510 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841555708152119296 |
|---|---|
| author | Osama Alkhazaleh |
| author_facet | Osama Alkhazaleh |
| author_sort | Osama Alkhazaleh |
| collection | DOAJ |
| description | This work employs a refined variation of the Homotopy Perturbation Method (HPM), termed the Modified Homotopy Perturbation Method (MHPM), designed to obtain accurate solutions for significant systems of partial differential equations (PDEs). By incorporating Laplace transforms and Padé approximants, MHPM achieves enhanced convergence and precision with minimal computational overhead, overcoming limitations of traditional perturbation techniques. We extend MHPM to solve more intricate nonlinear systems, showcasing its adaptability and robustness through applications to Burgers’ equations and the Brusselator model. These examples highlight MHPM’s utility in accurately resolving dynamic systems with real-world implications, including fluid flows, reaction kinetics, and engineering models, where computational efficiency and solution precision are critical. |
| format | Article |
| id | doaj-art-d481015efbc748bd85e5619b77d41aa2 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-d481015efbc748bd85e5619b77d41aa22025-01-08T04:53:46ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101065Modification of Homotopy Perturbation method for addressing systems of PDEsOsama Alkhazaleh0Department of Mathematics, Embry-Riddle Aeronautical University-Prescott Campus, Arizona 86301, USAThis work employs a refined variation of the Homotopy Perturbation Method (HPM), termed the Modified Homotopy Perturbation Method (MHPM), designed to obtain accurate solutions for significant systems of partial differential equations (PDEs). By incorporating Laplace transforms and Padé approximants, MHPM achieves enhanced convergence and precision with minimal computational overhead, overcoming limitations of traditional perturbation techniques. We extend MHPM to solve more intricate nonlinear systems, showcasing its adaptability and robustness through applications to Burgers’ equations and the Brusselator model. These examples highlight MHPM’s utility in accurately resolving dynamic systems with real-world implications, including fluid flows, reaction kinetics, and engineering models, where computational efficiency and solution precision are critical.http://www.sciencedirect.com/science/article/pii/S2666818124004510Modified Homotopy Perturbation MethodLaplace transformPadé approximantsAnalytic solutions |
| spellingShingle | Osama Alkhazaleh Modification of Homotopy Perturbation method for addressing systems of PDEs Partial Differential Equations in Applied Mathematics Modified Homotopy Perturbation Method Laplace transform Padé approximants Analytic solutions |
| title | Modification of Homotopy Perturbation method for addressing systems of PDEs |
| title_full | Modification of Homotopy Perturbation method for addressing systems of PDEs |
| title_fullStr | Modification of Homotopy Perturbation method for addressing systems of PDEs |
| title_full_unstemmed | Modification of Homotopy Perturbation method for addressing systems of PDEs |
| title_short | Modification of Homotopy Perturbation method for addressing systems of PDEs |
| title_sort | modification of homotopy perturbation method for addressing systems of pdes |
| topic | Modified Homotopy Perturbation Method Laplace transform Padé approximants Analytic solutions |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124004510 |
| work_keys_str_mv | AT osamaalkhazaleh modificationofhomotopyperturbationmethodforaddressingsystemsofpdes |