Reduced temporal convergence rates in high-order splitting schemes

2013/10/15 by M. T. Warnez, Warnez, M. T., Benson K. Muite +1
Engineering · Mathematics · #35K57 #65M12 #65M70 #Differential Equations and Numerical Methods #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1310.3901

openalex publication_date 2013/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Recently-derived high-order splitting schemes with complex coefficients are shown to exhibit reduced convergence rates for certain parabolic evolution equations. When applied to semilinear reaction-diffusion equations with periodic boundary conditions, these splitting schemes are most efficient when the diffusion terms are much less stiff than the reaction terms. An explanation for this is given in a simple setting.

Citations

• Fourth-Order Time-Stepping for Stiff PDEs

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