New Exact Solutions of Burgers’ Equation Using Power Index Method
In this article, we focus on the new exact solutions of Burger’s equation by using a new technique which is known as the power index method (PIM). In this method, we choose suitable indexes of independent variables and similarity transformation so that the partial differential equation may be conver...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2022/5211625 |
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| _version_ | 1832558564528357376 |
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| author | Khalil Ahmad Khudija Bibi |
| author_facet | Khalil Ahmad Khudija Bibi |
| author_sort | Khalil Ahmad |
| collection | DOAJ |
| description | In this article, we focus on the new exact solutions of Burger’s equation by using a new technique which is known as the power index method (PIM). In this method, we choose suitable indexes of independent variables and similarity transformation so that the partial differential equation may be converted into ODE. We have obtained analytic solution of the ODE by using symbolic package Maple. We have got exact solution of Burgers’ equation by using analytic solution of ODE and similarity transformation. The proposed method has been effectively employed to find new exact solutions for the nonlinear Burgers’ equation. Finally, the proposed resulting answers are compared with the homotopy perturbation, decomposition, and variational iteration solutions. |
| format | Article |
| id | doaj-art-063ea6ab3242458389b5a7db8347e1e0 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-063ea6ab3242458389b5a7db8347e1e02025-02-03T01:32:01ZengWileyDiscrete Dynamics in Nature and Society1607-887X2022-01-01202210.1155/2022/5211625New Exact Solutions of Burgers’ Equation Using Power Index MethodKhalil Ahmad0Khudija Bibi1Department of MathematicsDepartment of MathematicsIn this article, we focus on the new exact solutions of Burger’s equation by using a new technique which is known as the power index method (PIM). In this method, we choose suitable indexes of independent variables and similarity transformation so that the partial differential equation may be converted into ODE. We have obtained analytic solution of the ODE by using symbolic package Maple. We have got exact solution of Burgers’ equation by using analytic solution of ODE and similarity transformation. The proposed method has been effectively employed to find new exact solutions for the nonlinear Burgers’ equation. Finally, the proposed resulting answers are compared with the homotopy perturbation, decomposition, and variational iteration solutions.http://dx.doi.org/10.1155/2022/5211625 |
| spellingShingle | Khalil Ahmad Khudija Bibi New Exact Solutions of Burgers’ Equation Using Power Index Method Discrete Dynamics in Nature and Society |
| title | New Exact Solutions of Burgers’ Equation Using Power Index Method |
| title_full | New Exact Solutions of Burgers’ Equation Using Power Index Method |
| title_fullStr | New Exact Solutions of Burgers’ Equation Using Power Index Method |
| title_full_unstemmed | New Exact Solutions of Burgers’ Equation Using Power Index Method |
| title_short | New Exact Solutions of Burgers’ Equation Using Power Index Method |
| title_sort | new exact solutions of burgers equation using power index method |
| url | http://dx.doi.org/10.1155/2022/5211625 |
| work_keys_str_mv | AT khalilahmad newexactsolutionsofburgersequationusingpowerindexmethod AT khudijabibi newexactsolutionsofburgersequationusingpowerindexmethod |