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

Ryan I. Fernandes, Graeme Fairweather

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

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(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.

Original languageBritish English
Pages (from-to)6248-6267
Number of pages20
JournalJournal of Computational Physics
Volume231
Issue number19
DOIs
StatePublished - 1 Aug 2012

Keywords

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

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