On implicit algorithms of continuation method with applications to dynamic systems.

DOI10.1016/J.CAM.2003.11.010zbMath1042.65049OpenAlexW2080243235MaRDI QIDQ1426771

D. V. Snegovski, A. N. Danilin, D. B. Volkov-Bogorodskiy

Publication date: 15 March 2004

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

Full work available at URL: https://doi.org/10.1016/j.cam.2003.11.010

zbMATH Keywords

convergencenumerical examplesinitial value problemscontinuation methodRichardson extrapolationsecond order differential equationsdynamic systemsimplicit algorithmsautomatic step size controlsimple iterations

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Uses Software

• RODAS

Cites Work

• The Cauchy problem for mechanical systems with a finite number of degrees of freedom as a problem of continuation with respect to the best parameter
• The Cauchy problem as a problem of the continuation of a solution with respect to a parameter
• Solving Ordinary Differential Equations I
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