Hokkaido Mathematical Journal

WU Yu-Jiang, JIA Xing-Xing, SHE An-Long,

Semi-implicit schemes with multilevel wavelet-like incremental unknowns for solving reaction diffusion equation.

Hokkaido Mathematical Journal, 36 (2007) pp.711-728

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Abstract

Our aim in this paper is to present two types of emi-implicit schemes based on multilevel wavelet-like incremental unknowns (WIU) for solving a one-dimensional reaction-diffusion equation with a polynomial growth nonlinearity. The stability of schemes is proved which also shows the advantage over explicit and implicit schemes in the same conceptual framework of multilevel WIU. Numerical examples are provided to test the efficiency of the new schemes.

MSC(Primary)35K55
MSC(Secondary)65P40, 65M12, 65M06
Uncontrolled KeywordsWavelet-like incremental unknowns, reaction-diffusion equation, nonlinear Galerkin method, semi-implicit schemes