Survey of integral algorithms for ordinary differential equations

DOI10.1016/0096-3003(89)90112-4zbMath0675.65074OpenAlexW4244020868MaRDI QIDQ1122331

George F. Corliss

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0096-3003(89)90112-4

zbMATH Keywords

surveyinterval algorithmsinclusion of solutions

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Interval and finite arithmetic (65G30) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (8)

On a class of enclosure methods for initial value problems ⋮ Parallelotopic and practical observers for non-linear uncertain systems ⋮ Verified integration of linear \(n\)th order ODEs using large steps ⋮ On the stock estimation for a harvested fish population ⋮ Validated solutions of initial value problems for ordinary differential equations ⋮ An enclosure method for the solution of linear odes with polynomial coefficients ⋮ Rigorously computed orbits of dynamical systems without the wrapping effect ⋮ Passive robust fault detection using fuzzy parity equations

Uses Software

• DIFSUB
• Pascal-SC

Cites Work

• Asymptotic error expansions for defect correction iterates
• Iterated defect correction of differential equations. II: Numerical experiments
• Thirteen ways to estimate global error
• Automatic differentiation: techniques and applications
• The defect correction principle and discretization methods
• Using Interval Methods for the Numerical Solution of ODE's
• Adaptive, Self-Validating Numerical Quadrature
• Solving Ordinary Differential Equations Using Taylor Series
• On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations
• A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
• Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations
• Interpolants for Runge-Kutta formulas
• The automatic integration of ordinary differential equations
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