Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order
Autor: | Kuppalapalle Vajravelu, F. Talay Akyildiz |
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Rok vydání: | 2018 |
Předmět: |
General Computer Science
Discretization Applied Mathematics 010103 numerical & computational mathematics Space (mathematics) 01 natural sciences Parabolic partial differential equation Backward Euler method Chebyshev filter 010305 fluids & plasmas Modeling and Simulation 0103 physical sciences Applied mathematics Pseudo-spectral method 0101 mathematics Temporal discretization Galerkin method Engineering (miscellaneous) Mathematics |
Zdroj: | Applied Mathematics and Nonlinear Sciences. 3:255-264 |
ISSN: | 2444-8656 |
Popis: | In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems. |
Databáze: | OpenAIRE |
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