Approximate Solutions of Fisher's Type Equations with Variable Coefficients
The spectral collocation approximations based on Legendre polynomials are used to compute the numerical solution of time-dependent Fisher’s type problems. The spatial derivatives are collocated at a Legendre-Gauss-Lobatto interpolation nodes. The proposed method has the advantage of reducing the pro...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/176730 |
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| author | A. H. Bhrawy M. A. Alghamdi |
| author_facet | A. H. Bhrawy M. A. Alghamdi |
| author_sort | A. H. Bhrawy |
| collection | DOAJ |
| description | The spectral collocation approximations based on Legendre polynomials are used to compute the numerical solution of time-dependent Fisher’s type problems. The spatial derivatives are collocated at a Legendre-Gauss-Lobatto interpolation nodes. The proposed method has the advantage of reducing the problem to a system of ordinary differential equations in time. The four-stage A-stable implicit Runge-Kutta scheme is applied to solve the resulted system of first order in time. Numerical results show that the Legendre-Gauss-Lobatto collocation method is of high accuracy and is efficient for solving the Fisher’s type equations. Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations. |
| format | Article |
| id | doaj-art-67f46e616f934cf180b688952756f46d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-67f46e616f934cf180b688952756f46d2025-02-03T01:09:40ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/176730176730Approximate Solutions of Fisher's Type Equations with Variable CoefficientsA. H. Bhrawy0M. A. Alghamdi1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaThe spectral collocation approximations based on Legendre polynomials are used to compute the numerical solution of time-dependent Fisher’s type problems. The spatial derivatives are collocated at a Legendre-Gauss-Lobatto interpolation nodes. The proposed method has the advantage of reducing the problem to a system of ordinary differential equations in time. The four-stage A-stable implicit Runge-Kutta scheme is applied to solve the resulted system of first order in time. Numerical results show that the Legendre-Gauss-Lobatto collocation method is of high accuracy and is efficient for solving the Fisher’s type equations. Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.http://dx.doi.org/10.1155/2013/176730 |
| spellingShingle | A. H. Bhrawy M. A. Alghamdi Approximate Solutions of Fisher's Type Equations with Variable Coefficients Abstract and Applied Analysis |
| title | Approximate Solutions of Fisher's Type Equations with Variable Coefficients |
| title_full | Approximate Solutions of Fisher's Type Equations with Variable Coefficients |
| title_fullStr | Approximate Solutions of Fisher's Type Equations with Variable Coefficients |
| title_full_unstemmed | Approximate Solutions of Fisher's Type Equations with Variable Coefficients |
| title_short | Approximate Solutions of Fisher's Type Equations with Variable Coefficients |
| title_sort | approximate solutions of fisher s type equations with variable coefficients |
| url | http://dx.doi.org/10.1155/2013/176730 |
| work_keys_str_mv | AT ahbhrawy approximatesolutionsoffisherstypeequationswithvariablecoefficients AT maalghamdi approximatesolutionsoffisherstypeequationswithvariablecoefficients |