One-leg Integration of Ordinary Differential Equations with Global Error Control

DOI10.2478/cmam-2005-0004zbMath1070.65056OpenAlexW2086647459MaRDI QIDQ4680003

G. Yu. Kulikov, Sergey K. Shindin

Publication date: 31 May 2005

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

Full work available at URL: https://doi.org/10.2478/cmam-2005-0004

zbMATH Keywords

numerical examples\(A\)-stabilityerror controlstiff problems\(G\)-stabilityone-leg multistep methodsglobal error evaluationlocal error evaluationlocal-global step size control

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stochastic approximation (62L20) 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)

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Entropy dissipative one‐leg multistep time approximations of nonlinear diffusive equations ⋮ One-leg variable-coefficient formulas for ordinary differential equations and local-global step size control ⋮ Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow ⋮ Automatic step size and order control in implicit one-step extrapolation methods ⋮ One-leg methods for nonlinear stiff fractional differential equations with Caputo derivatives ⋮ Refactorization of a variable step, unconditionally stable method of Dahlquist, Liniger and Nevanlinna ⋮ Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems

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