Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes

DOI10.1016/j.cam.2007.02.034zbMath1149.65052OpenAlexW2062406587MaRDI QIDQ932720

S. González-Pinto, Juan I. Montijano, Manuel Calvo

Publication date: 11 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.cam.2007.02.034

zbMATH Keywords

adaptive methodsRunge-Kutta methodsglobal error estimatestolerance proportionality

Mathematics Subject Classification ID

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)

Related Items (7)

Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods ⋮ 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 ⋮ A transformation method for solving conservative nonlinear two-degree-of-freedom systems ⋮ 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 ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

• ODEPACK

Cites Work

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• A Code Based on the Two-Stage Runge-Kutta Gauss Formula for Second-Order Initial Value Problems
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• Global Error versus Tolerance for Explicit Runge-Kutta Methods
• Robust Defect Control with Runge–Kutta Schemes
• Global error estimation with adaptive explicit Runge-Kutta methods

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