On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets
In this work, we design, analyze, and test an efficient algorithm based on the finite difference method and wavelet Galerkin method to solve the well known Fisher's equation. We employed the Crank-Nicolson scheme to discretize the time interval into a finite number of time steps, and this gives...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021144?viewType=HTML |
| _version_ | 1818412534774890496 |
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| author | Haifa Bin Jebreen |
| author_facet | Haifa Bin Jebreen |
| author_sort | Haifa Bin Jebreen |
| collection | DOAJ |
| description | In this work, we design, analyze, and test an efficient algorithm based on the finite difference method and wavelet Galerkin method to solve the well known Fisher's equation. We employed the Crank-Nicolson scheme to discretize the time interval into a finite number of time steps, and this gives rise to an ordinary differential equation at each time step. To solve this ODE, we utilize the multiwavelets Galerkin method. The L<sub>2</sub> stability and convergence of the scheme have been investigated by the energy method. Illustrative examples are provided to verify the efficiency and applicability of the method. |
| first_indexed | 2024-12-14T10:48:51Z |
| format | Article |
| id | doaj.art-76ea1a808b9943ba83d661debaac0ca5 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-14T10:48:51Z |
| publishDate | 2021-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-76ea1a808b9943ba83d661debaac0ca52022-12-21T23:05:20ZengAIMS PressAIMS Mathematics2473-69882021-01-01632369238410.3934/math.2021144On the numerical solution of Fisher's equation by an efficient algorithm based on multiwaveletsHaifa Bin Jebreen0Department of mathematics, College of science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaIn this work, we design, analyze, and test an efficient algorithm based on the finite difference method and wavelet Galerkin method to solve the well known Fisher's equation. We employed the Crank-Nicolson scheme to discretize the time interval into a finite number of time steps, and this gives rise to an ordinary differential equation at each time step. To solve this ODE, we utilize the multiwavelets Galerkin method. The L<sub>2</sub> stability and convergence of the scheme have been investigated by the energy method. Illustrative examples are provided to verify the efficiency and applicability of the method.http://www.aimspress.com/article/doi/10.3934/math.2021144?viewType=HTMLwavelet galerkin methodmultiwaveletsenergy methodfisher's equation |
| spellingShingle | Haifa Bin Jebreen On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets AIMS Mathematics wavelet galerkin method multiwavelets energy method fisher's equation |
| title | On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets |
| title_full | On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets |
| title_fullStr | On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets |
| title_full_unstemmed | On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets |
| title_short | On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets |
| title_sort | on the numerical solution of fisher s equation by an efficient algorithm based on multiwavelets |
| topic | wavelet galerkin method multiwavelets energy method fisher's equation |
| url | http://www.aimspress.com/article/doi/10.3934/math.2021144?viewType=HTML |
| work_keys_str_mv | AT haifabinjebreen onthenumericalsolutionoffishersequationbyanefficientalgorithmbasedonmultiwavelets |