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• W2034809969 abstract "An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only $O({cal N})$ operations where ${cal N}$ is the number of unknowns. Moreover,it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties." @default.
• W2034809969 created "2016-06-24" @default.
• W2034809969 creator A5056234867 @default.
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• W2034809969 date "2012-08-01" @default.
• W2034809969 modified "2023-09-26" @default.
• W2034809969 title "An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction–diffusion systems" @default.
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• W2034809969 doi "https://doi.org/10.1016/j.jcp.2012.04.001" @default.
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