A simple step size selection algorithm for ODE codes

DOI10.1016/0377-0427(94)00007-NzbMath0842.65052OpenAlexW2058817453MaRDI QIDQ1899962

Yanyan Li

Publication date: 5 August 1996

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

Full work available at URL: https://doi.org/10.1016/0377-0427(94)00007-n

zbMATH Keywords

algorithmlocal errorstepsize controlglobal errorlocal error estimate

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (7)

Extended scaling invariance of one-dimensional models of liquid dynamics in a horizontal capillary ⋮ Piecewise-linearized methods for initial-value problems ⋮ A Fortran 90 separable Hamiltonian system solver ⋮ Error estimation and control for ODEs ⋮ Piecewise-linearized and linearized \(\vartheta\)-methods for ordinary and partial differential equations. ⋮ Adaptive stiff solvers at low accuracy and complexity ⋮ Fully implicit solution of large-scale non-equilibrium radiation diffusion with high order time integration

Cites Work

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• Error estimators for stiff differential equations
• The step sizes used by one-step codes for ODEs
• Starting step size for an ODE solver
• Practical improvements to SIMPR codes for stiff ODEs
• Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
• The design of a variable-step integrator for the simulation of gas transmission networks
• Runge-Kutta Methods with Minimum Error Bounds
• An Attempt to Avoid Exact Jacobian and Nonlinear Equations in the Numerical Solution of Stiff Differential Equations
• SomeL-stable methods for stiff differential equations
• On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations
• Solving Nonstiff Ordinary Differential Equations—The State of the Art
• Comparing Numerical Methods for Ordinary Differential Equations
• Comparing Error Estimators for Runge-Kutta Methods

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