Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics
In this paper, we studied and analysed a new iterative method for solving time-fractional non-linear equations by obtaining approximate solutions to the Allen-Cahn, Newell-Whitehead, and Fisher equations by putting the parameter \alpha = 1 and varying the values of \gamma, \phi, and \tau. These thre...
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| Language: | English |
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Nigerian Society of Physical Sciences
2024-05-01
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| Series: | African Scientific Reports |
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| Online Access: | https://asr.nsps.org.ng/index.php/asr/article/view/176 |
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| author | K. Issa R. A. Bello M. H. Sulaiman |
| author_facet | K. Issa R. A. Bello M. H. Sulaiman |
| author_sort | K. Issa |
| collection | DOAJ |
| description | In this paper, we studied and analysed a new iterative method for solving time-fractional non-linear equations by obtaining approximate solutions to the Allen-Cahn, Newell-Whitehead, and Fisher equations by putting the parameter \alpha = 1 and varying the values of \gamma, \phi, and \tau. These three equations were derived from the general non-linear dynamical wave equations when the constants therein assumed certain specific values. Obviously, from the tabulated results, we observed that the approximate solution for each example compares favourably with the existing results in the literature; therefore, the proposed scheme is effective and accurate in solving Allen-Cahn, Newell-Whitehead, and Fisher equations. All the computational work was done using Mathematica, and all the graphs were plotted using MATLAB.
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| format | Article |
| id | doaj-art-683fcf7c5c8d4a64aa75e75ad091f9d8 |
| institution | DOAJ |
| issn | 2955-1625 2955-1617 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | Article |
| series | African Scientific Reports |
| spelling | doaj-art-683fcf7c5c8d4a64aa75e75ad091f9d82025-08-20T03:09:27ZengNigerian Society of Physical SciencesAfrican Scientific Reports2955-16252955-16172024-05-013210.46481/asr.2024.3.2.176Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical PhysicsK. IssaR. A. BelloM. H. SulaimanIn this paper, we studied and analysed a new iterative method for solving time-fractional non-linear equations by obtaining approximate solutions to the Allen-Cahn, Newell-Whitehead, and Fisher equations by putting the parameter \alpha = 1 and varying the values of \gamma, \phi, and \tau. These three equations were derived from the general non-linear dynamical wave equations when the constants therein assumed certain specific values. Obviously, from the tabulated results, we observed that the approximate solution for each example compares favourably with the existing results in the literature; therefore, the proposed scheme is effective and accurate in solving Allen-Cahn, Newell-Whitehead, and Fisher equations. All the computational work was done using Mathematica, and all the graphs were plotted using MATLAB. https://asr.nsps.org.ng/index.php/asr/article/view/176Iterative methodGamma functionParabolic equation |
| spellingShingle | K. Issa R. A. Bello M. H. Sulaiman Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics African Scientific Reports Iterative method Gamma function Parabolic equation |
| title | Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics |
| title_full | Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics |
| title_fullStr | Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics |
| title_full_unstemmed | Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics |
| title_short | Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics |
| title_sort | approximate solution of time fractional non linear parabolic equations arising in mathematical physics |
| topic | Iterative method Gamma function Parabolic equation |
| url | https://asr.nsps.org.ng/index.php/asr/article/view/176 |
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