Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations
| Autor: | Boying Wu, Jiebao Sun, Wenjie Liu |
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| Rok vydání: | 2015 |
| Předmět: |
Discretization
Applied Mathematics Numerical analysis Mathematical analysis 010103 numerical & computational mathematics 01 natural sciences Parabolic partial differential equation Mathematics::Numerical Analysis 010101 applied mathematics Convergence (routing) A priori and a posteriori 0101 mathematics Temporal discretization Spectral method Galerkin method Mathematics |
| Zdroj: | Numerical Algorithms. 71:437-455 |
| ISSN: | 1572-9265 1017-1398 |
| DOI: | 10.1007/s11075-015-0002-x |
| Popis: | In this paper, we present a high-order accurate method for two-dimensional semilinear parabolic equations. The method is based on a Galerkin-Chebyshev spectral method for discretizing spatial derivatives and a block boundary value methods of fourth-order for temporal discretization. Our formulation has high-order accurate in both space and time. Optimal a priori error bound is derived in the weighted L?2$L^{2}_{\omega }$-norm for the semidiscrete formulation. Extensive numerical results are presented to demonstrate the convergence properties of the method. |
| Databáze: | OpenAIRE |
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