A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods
| Autor: | Kourosh Parand, Mehran Nikarya |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discretization
Numerical analysis General Physics and Astronomy 010103 numerical & computational mathematics Krylov subspace 01 natural sciences 010305 fluids & plasmas Algebraic equation Nonlinear system symbols.namesake Linearization Collocation method 0103 physical sciences symbols Applied mathematics 0101 mathematics Bessel function Mathematics |
| Zdroj: | The European Physical Journal Plus. 132 |
| ISSN: | 2190-5444 |
| DOI: | 10.1140/epjp/i2017-11787-x |
| Popis: | In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods. |
| Databáze: | OpenAIRE |
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