On the change of step size in multistep codes

DOI10.1007/BF02144108zbMath0779.65055OpenAlexW1994896249MaRDI QIDQ1208710

Manuel Calvo, Luis Rández, Juan I. Montijano

Publication date: 16 May 1993

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02144108

zbMATH Keywords

numerical experimentsstep size controlmultistep methodsbackward differentiation formulalocal discretization errorAdams type methodsFLC methodsstep size selection algorithms

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (9)

Convergence of the variable two-step BDF time discretisation of nonlinear evolution problems governed by a monotone potential operator ⋮ A generalization to variable stepsizes of Störmer methods for second-order differential equations ⋮ An embedded 3(2) pair of nonlinear methods for solving first order initial-value ordinary differential systems ⋮ A robust optimization approach to experimental design for model discrimination of dynamical systems ⋮ Unnamed Item ⋮ A numerical ODE solver that preserves the fixed points and their stability ⋮ Numerical solution of nonlinear singularly perturbed problems by using a non-standard algorithm on variable stepsize implementation (CMMSE-2009) ⋮ Solving first-order initial-value problems by using an explicit non-standard \(A\)-stable one-step method in variable step-size formulation ⋮ A unified approach for the development of \(k\)-step block Falkner-type methods for solving general second-order initial-value problems in ODEs

Uses Software

• VODE

Cites Work

• VODE: A Variable-Coefficient ODE Solver
• The Effect of Changing the Stepsize in Linear Multistep Codes
• An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs
• A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
• Algorithms for Changing the Step Size
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