On the local and global errors of splitting approximations of reaction–diffusion equations with high spatial gradients

DOI10.1080/00207160701458716zbMath1122.65061OpenAlexW2109866862MaRDI QIDQ3595047

Thierry Dumont, Marc Massot, Violaine Louvet, Stéphane Descombes

Publication date: 10 August 2007

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160701458716

zbMATH Keywords

error estimatessemidiscretizationreaction-diffusion equationsplitting methodstiff problemhigh spatial gradient

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (4)

Discontinuous Galerkin \(h p\)-adaptive methods for multiscale chemical reactors: quiescent reactors ⋮ An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime ⋮ Local error estimates for adaptive simulation of the reaction-diffusion master equation via operator splitting ⋮ Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures

Uses Software

• ODEPACK

Cites Work

• Traveling-wave solutions of parabolic systems with discontinuous nonlinear terms
• Strang's formula for holomorphic semi-groups
• Error bounds for exponential operator splittings
• On the convergence and optimization of the Baker-Campbell-Hausdorff formula
• Accurate partial difference methods. I: Linear Cauchy problems
• Convergence of a splitting method of high order for reaction-diffusion systems
• On the Construction and Comparison of Difference Schemes
• The norm convergence of the Trotter-Kato product formula with error bound

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