Jacobi–Gauss–Lobatto collocation method for solving nonlinear reaction–diffusion equations subject to Dirichlet boundary conditions
This paper extends the application of the spectral Jacobi–Gauss–Lobatto collocation (J-GL-C) method based on Gauss–Lobatto nodes to obtain semi-analytical solutions of nonlinear time-dependent reaction–diffusion equations (RDEs) subject to Dirichlet boundary conditions. This approach has the advanta...
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| Published in | Applied mathematical modelling Vol. 40; no. 3; pp. 1703 - 1716 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
01.02.2016
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| ISSN | 0307-904X |
| DOI | 10.1016/j.apm.2015.09.009 |
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| Abstract | This paper extends the application of the spectral Jacobi–Gauss–Lobatto collocation (J-GL-C) method based on Gauss–Lobatto nodes to obtain semi-analytical solutions of nonlinear time-dependent reaction–diffusion equations (RDEs) subject to Dirichlet boundary conditions. This approach has the advantage of allowing us to obtain the solution in terms of the Jacobi parameters α and β, which therefore means that the method holds a number of collocation methods as a special case. In addition, the problem is reduced to the solution of system of ordinary differential equations (SODEs) in the time variable, which may then be solved by any standard numerical technique. We consider five applications of the general method to concrete examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving nonlinear time-dependent RDEs. |
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| AbstractList | This paper extends the application of the spectral Jacobi–Gauss–Lobatto collocation (J-GL-C) method based on Gauss–Lobatto nodes to obtain semi-analytical solutions of nonlinear time-dependent reaction–diffusion equations (RDEs) subject to Dirichlet boundary conditions. This approach has the advantage of allowing us to obtain the solution in terms of the Jacobi parameters α and β, which therefore means that the method holds a number of collocation methods as a special case. In addition, the problem is reduced to the solution of system of ordinary differential equations (SODEs) in the time variable, which may then be solved by any standard numerical technique. We consider five applications of the general method to concrete examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving nonlinear time-dependent RDEs. |
| Author | Doha, E.H. Abdelkawy, M.A. Van Gorder, R.A. Bhrawy, A.H. |
| Author_xml | – sequence: 1 givenname: A.H. surname: Bhrawy fullname: Bhrawy, A.H. email: alibhrawy@yahoo.co.uk organization: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia – sequence: 2 givenname: E.H. surname: Doha fullname: Doha, E.H. email: eiddoha@frcu.eun.eg organization: Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt – sequence: 3 givenname: M.A. surname: Abdelkawy fullname: Abdelkawy, M.A. email: melkawy@yahoo.com organization: Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt – sequence: 4 givenname: R.A. surname: Van Gorder fullname: Van Gorder, R.A. email: Robert.VanGorder@maths.ox.ac.uk organization: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG United Kingdom |
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| Snippet | This paper extends the application of the spectral Jacobi–Gauss–Lobatto collocation (J-GL-C) method based on Gauss–Lobatto nodes to obtain semi-analytical... |
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| SubjectTerms | Collocation method Jacobi–Gauss–Lobatto quadrature Nonlinear reaction–diffusion equations |
| Title | Jacobi–Gauss–Lobatto collocation method for solving nonlinear reaction–diffusion equations subject to Dirichlet boundary conditions |
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