A new approach to error estimation for general linear methods

DOI10.1007/s00211-002-0452-7zbMath1032.65088OpenAlexW2095180669MaRDI QIDQ1412175

John C. Butcher, Zdzisław Jackiewicz

Publication date: 9 November 2003

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-002-0452-7

zbMATH Keywords

error estimatesstepsize controlGeneral linear methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) 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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (16)

A new approach to the construction of DIMSIMs of high order and stage order ⋮ Towards a code for nonstiff differential systems based on general linear methods with inherent Runge-Kutta stability ⋮ Error propagation for implicit-explicit general linear methods ⋮ Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods ⋮ Construction and implementation of general linear methods for ordinary differential equations: a review ⋮ Strong stability preserving general linear methods ⋮ Explicit Nordsieck methods with extended stability regions ⋮ ``Rescale and modify implementation of IRKS methods ⋮ Order conditions for general linear methods ⋮ Error propagation of general linear methods for ordinary differential equations ⋮ Search for efficient general linear methods for ordinary differential equations ⋮ Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations ⋮ General linear methods for ordinary differential equations ⋮ A new class of efficient general linear methods for ordinary differential equations ⋮ Variable order and stepsize in general linear methods ⋮ Global error estimation for explicit general linear methods

Uses Software

• DIMSIM

This page was built for publication: A new approach to error estimation for general linear methods