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Semi‐implicit spectral collocation methods for reaction‐diffusion equations on annuli
Author(s) -
Liu Jiangguo,
Tavener Simon
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20572
Subject(s) - mathematics , spectral method , collocation method , chebyshev filter , partial differential equation , collocation (remote sensing) , nonlinear system , reaction–diffusion system , chebyshev polynomials , diffusion , mathematical analysis , differential equation , computer science , physics , ordinary differential equation , machine learning , thermodynamics , quantum mechanics
In this article, we develop numerical schemes for solving stiff reaction‐diffusion equations on annuli based on Chebyshev and Fourier spectral spatial discretizations and integrating factor methods for temporal discretizations. Stiffness is resolved by treating the linear diffusion through the use of integrating factors and the nonlinear reaction term implicitly. Root locus curves provide a succinct analysis of the A‐stability of these schemes. By utilizing spectral collocation methods, we avoid the use of potentially expensive transforms between the physical and spectral spaces. Numerical experiments are presented to illustrate the accuracy and efficiency of these schemes. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1113–1129, 2011