Numerical investigations on global error estimation for ordinary differential equations

DOI10.1016/S0377-0427(97)00079-4zbMath0887.65096OpenAlexW2081224448MaRDI QIDQ1372048

Laurent Levacher, René Aïd

Publication date: 27 May 1998

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(97)00079-4

zbMATH Keywords

numerical examplesRichardson extrapolationtest problemsglobal error estimationZadunaisky method

Mathematics Subject Classification ID

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)

Related Items (15)

Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods ⋮ Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation ⋮ Local theory of extrapolation methods ⋮ Variable-stepsize doubly quasi-consistent singly diagonally implicit two-step peer pairs for solving stiff ordinary differential equations ⋮ Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods ⋮ Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods ⋮ Automatic step size and order control in implicit one-step extrapolation methods ⋮ Nested implicit Runge-Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equations ⋮ Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control ⋮ Global error estimation and control in linearly-implicit parallel two-step peer W-methods ⋮ 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 ⋮ Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

• VODE

Cites Work

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