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Stability of operator splitting methods for systems with indefinite operators: Reaction-diffusion systems. (English) Zbl 1073.65088
The authors present an analysis of the stability of operator-splitting methods for systems with indefinite operators, including negative definite systems with an indefinite component operator and indefinite systems. The result of this analysis demonstrates the importance of the spectral decay properties of the amplification factors of the integration of the diffusion operator. The results are used to explore the convergence and it is shown experimentally that if the method used for the diffusion then high wave number modes will pollute the solution.

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
Software:
CVODE
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