An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis Technique
The current work aims to study a new analytical solution method for a family of Kuramoto–Sivashinsky equation (KSE). For this purpose, we implement the q-homotopy analysis method (q-HAM), a method extensively used due to its easy implementation, fast convergence, and presence of convergence-controll...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2024/6652990 |
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| _version_ | 1832544015345516544 |
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| author | Abdullah Shah Safdar Hussain |
| author_facet | Abdullah Shah Safdar Hussain |
| author_sort | Abdullah Shah |
| collection | DOAJ |
| description | The current work aims to study a new analytical solution method for a family of Kuramoto–Sivashinsky equation (KSE). For this purpose, we implement the q-homotopy analysis method (q-HAM), a method extensively used due to its easy implementation, fast convergence, and presence of convergence-controlling parameters. This method does not require any transformation, linearization, or discretization. The applied method offers a well-convergent series solution. Results are obtained for some fixed values of physically significant parameters involved in the mathematical model. The computed results are compared with the travelling wave solutions and are illustrated graphically and in tabulated form for absolute error estimation. The comparison reveals the q-HAM provides better results than the existing methods. |
| format | Article |
| id | doaj-art-bcbc269b600747278dd7bf6d33879257 |
| institution | Kabale University |
| issn | 1687-9651 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-bcbc269b600747278dd7bf6d338792572025-02-03T11:13:37ZengWileyInternational Journal of Differential Equations1687-96512024-01-01202410.1155/2024/6652990An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis TechniqueAbdullah Shah0Safdar Hussain1Department of MathematicsDepartment of Mathematical SciencesThe current work aims to study a new analytical solution method for a family of Kuramoto–Sivashinsky equation (KSE). For this purpose, we implement the q-homotopy analysis method (q-HAM), a method extensively used due to its easy implementation, fast convergence, and presence of convergence-controlling parameters. This method does not require any transformation, linearization, or discretization. The applied method offers a well-convergent series solution. Results are obtained for some fixed values of physically significant parameters involved in the mathematical model. The computed results are compared with the travelling wave solutions and are illustrated graphically and in tabulated form for absolute error estimation. The comparison reveals the q-HAM provides better results than the existing methods.http://dx.doi.org/10.1155/2024/6652990 |
| spellingShingle | Abdullah Shah Safdar Hussain An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis Technique International Journal of Differential Equations |
| title | An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis Technique |
| title_full | An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis Technique |
| title_fullStr | An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis Technique |
| title_full_unstemmed | An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis Technique |
| title_short | An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis Technique |
| title_sort | analytical approach to the new solution of family of kuramoto sivashinsky equation by q homotopy analysis technique |
| url | http://dx.doi.org/10.1155/2024/6652990 |
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