An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems

作者：Fernandes Ryan I; Fairweather Graeme^*

来源：Journal of Computational Physics, 2012, 231(19): 6248-6267.

DOI：10.1016/j.jcp.2012.04.001

• Nonlinear reaction-diffusion systems
• Alternating direction implicit method
• Orthogonal spline collocation
• Extrapolated Crank-Nicolson method
• Brusselator
• Gray-Scott
• Gierer-Meinhardt
• Schnakenberg models

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(N) operations where 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.

• 出版日期2012-8-1