Error analysis of variable stepsize Runge-Kutta methods for a class of multiply-stiff singular perturbation problems

DOI10.1016/j.camwa.2006.06.009zbMath1130.65084OpenAlexW2088188633MaRDI QIDQ2458729

Ai-Guo Xiao

Publication date: 2 November 2007

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.06.009

zbMATH Keywords

convergencesingular perturbationnumerical exampleserror boundsRunge-Kutta methodsvariable stepsizemultiple-stiffness

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) 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)

Uses Software

• RODAS

Cites Work

• B-convergence of Lobatto IIIC formulas
• On error behaviour of partitioned linearly implicit Runge-Kutta methods for stiff and differential algebraic systems
• Matrix valued versions of a result of von Neumann with an application to time discretization
• 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
• Order results for Rosenbrock type methods on classes of stiff equations
• On the convergence of Runge-Kutta methods for stiff nonlinear differential equations
• Convergence results for general linear methods on singular perturbation problems
• On the numerical solution of stiff IVPs by Lobatto IIIA Runge-Kutta methods
• Runge-Kutta methods for the numerical solution of stiff semilinear systems
• Error of partitioned Runge-Kutta methods for multiple stiff singular perturbation problems
• The error committed by stopping the Newton iteration in the numerical solution of stiff initial value problems
• Convergence results of one-leg and linear multistep methods for multiply stiff singular perturbation problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item