Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations
A new scheme, deduced from Khan’s homotopy perturbation transform method (HPTM) (Khan, 2014; Khan and Wu, 2011) via optimal parameter, is presented for solving nonlinear differential difference equations. Simple but typical examples are given to illustrate the validity and great potential of Khan’s...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/813474 |
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| author | Mohamed S. Mohamed Khaled A. Gepreel Faisal A. Al-Malki Nouf Altalhi |
| author_facet | Mohamed S. Mohamed Khaled A. Gepreel Faisal A. Al-Malki Nouf Altalhi |
| author_sort | Mohamed S. Mohamed |
| collection | DOAJ |
| description | A new scheme, deduced from Khan’s homotopy perturbation transform method (HPTM) (Khan, 2014; Khan and Wu, 2011) via optimal parameter, is presented for solving nonlinear differential difference equations. Simple but typical examples are given to illustrate the validity and great potential of Khan’s homotopy perturbation transform method (HPTM) via optimal parameter in solving nonlinear differential difference equation. The numerical solutions show that the proposed method is very efficient and computationally attractive.
It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems. The results reveal that the method is very effective and simple. This method gives more reliable results as compared to other existing methods available in the literature. The numerical results demonstrate the validity and applicability of the method. |
| format | Article |
| id | doaj-art-9cbc455089d1464c96efa034f793f4a9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9cbc455089d1464c96efa034f793f4a92025-02-03T06:07:28ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/813474813474Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference EquationsMohamed S. Mohamed0Khaled A. Gepreel1Faisal A. Al-Malki2Nouf Altalhi3Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Taif University, Taif, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Taif University, Taif, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Taif University, Taif, Saudi ArabiaA new scheme, deduced from Khan’s homotopy perturbation transform method (HPTM) (Khan, 2014; Khan and Wu, 2011) via optimal parameter, is presented for solving nonlinear differential difference equations. Simple but typical examples are given to illustrate the validity and great potential of Khan’s homotopy perturbation transform method (HPTM) via optimal parameter in solving nonlinear differential difference equation. The numerical solutions show that the proposed method is very efficient and computationally attractive. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems. The results reveal that the method is very effective and simple. This method gives more reliable results as compared to other existing methods available in the literature. The numerical results demonstrate the validity and applicability of the method.http://dx.doi.org/10.1155/2014/813474 |
| spellingShingle | Mohamed S. Mohamed Khaled A. Gepreel Faisal A. Al-Malki Nouf Altalhi Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations Journal of Applied Mathematics |
| title | Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations |
| title_full | Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations |
| title_fullStr | Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations |
| title_full_unstemmed | Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations |
| title_short | Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations |
| title_sort | extension of khan s homotopy transformation method via optimal parameter for differential difference equations |
| url | http://dx.doi.org/10.1155/2014/813474 |
| work_keys_str_mv | AT mohamedsmohamed extensionofkhanshomotopytransformationmethodviaoptimalparameterfordifferentialdifferenceequations AT khaledagepreel extensionofkhanshomotopytransformationmethodviaoptimalparameterfordifferentialdifferenceequations AT faisalaalmalki extensionofkhanshomotopytransformationmethodviaoptimalparameterfordifferentialdifferenceequations AT noufaltalhi extensionofkhanshomotopytransformationmethodviaoptimalparameterfordifferentialdifferenceequations |