The tolerance proportionality of adaptive ODE solvers

DOI10.1016/0377-0427(93)90277-IzbMath0780.65050MaRDI QIDQ688621

Desmond J. Higham

Publication date: 23 January 1994

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

interpolationexplicit Runge-Kutta methodsglobal errorerror tolerancedelay ordinary differential equationserror control methodtolerance proportionality

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 (12)

Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods ⋮ Equilibrium states of adaptive algorithms for delay differential equations ⋮ New third- and fourth-order singly diagonally implicit two-step peer triples with local and global error controls for solving stiff ordinary differential equations ⋮ Variable-stepsize doubly quasi-consistent singly diagonally implicit two-step peer pairs for solving stiff ordinary differential equations ⋮ Nested implicit Runge-Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equations ⋮ Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes ⋮ Local and global error estimation and control within explicit two-step peer triples ⋮ NIRK-based Cholesky-factorized square-root accurate continuous-discrete unscented Kalman filters for state estimation in nonlinear continuous-time stochastic models with discrete measurements ⋮ Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations ⋮ Projection methods preserving Lyapunov functions ⋮ Optimal residuals and the Dahlquist test problem ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

• Matlab

Cites Work

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• Error control for initial value problems with discontinuities and delays
• Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method
• General framework, stability and error analysis for numerical stiff boundary value methods
• A new error-control for initial value solvers
• Local error control in codes for ordinary differential equations
• Global Error versus Tolerance for Explicit Runge-Kutta Methods
• Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods

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