The behaviour of the local error in splitting methods applied to stiff problems

DOI10.1016/j.jcp.2003.10.011zbMath1053.65061OpenAlexW1978122310MaRDI QIDQ598339

Sumit K. Garg

Publication date: 6 August 2004

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2003.10.011

zbMATH Keywords

consistencynumerical experimentserror controlstiff differential equationsSingular perturbationGeometric integrationLie seriesstepsize selectionOrder reductionSplitting methodsTime integration

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Singular perturbations for ordinary differential equations (34E15) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (10)

The error structure of the Douglas-Rachford splitting method for stiff linear problems ⋮ Averaging operators for exponential splittings ⋮ Symmetric-conjugate splitting methods for evolution equations of parabolic type ⋮ 3DFLUX: a high-order fully three-dimensional flux integral solver for the scalar transport equation ⋮ A variational splitting integrator for quantum molecular dynamics. ⋮ An iterative semi-implicit scheme with robust damping ⋮ A fully adaptive reaction-diffusion integration scheme with applications to systems biology ⋮ On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations ⋮ Operator splitting for chemical reaction systems with fast chemistry ⋮ A novel approach to rigid spheroid models in viscous flows using operator splitting methods

Uses Software

• RODAS

Cites Work

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• Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
• Error of Rosenbrock methods for stiff problems studied via differential algebraic equations
• Error bounds for exponential operator splittings
• Rosenbrock methods for differential algebraic equations
• Convergence of a splitting method of high order for reaction-diffusion systems
• Splitting methods
• The Concept of B-Convergence
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
• On the Construction and Comparison of Difference Schemes

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