Second-order implicit-explicit scheme for the Gray-Scott model

Authors:
Kai Zhang;Jeff C. -F. Wong;Ran Zhang
Affiliations:
Department of Mathematics, Jilin University, Changchun, Jilin, 130023, PR China;Department of Mathematics, The Chinese University of Hong Kong, Lady Shaw Building, Rm 208, Shatin N.T., Hong Kong;Department of Mathematics, Jilin University, Changchun, Jilin, 130023, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

A second-order scheme for the Gray-Scott (GS) model used to describe the pattern formation is studied. The linear part of the GS equation for the time derivative and the viscous terms is discretized implicitly, while the other (or nonlinear) part of the GS equation explicitly. Galerkin finite element approximation methods are presented and analyzed, as well as methods for solving the resulting system of equations. The optimal L^2-norm error estimates are derived. Numerical experiments are presented.