Stability of operator splitting methods for systems with indefinite operators: Reaction-diffusion systems (Q1777077)

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.