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Convergence of a splitting method of high order for reaction-diffusion systems. (English) Zbl 0981.65107
Author’s summary: We prove the convergence of a splitting scheme of high-order for a reaction-diffusion system of the form $u_t- M\Delta u+ F(u)= 0,$ where $$M$$ is an $$m\times m$$ matrix whose spectrum is included in $$\{\text{Re }z> 0\}$$. This scheme is obtained by applying a Richardson extrapolation to a Strang formula.

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