Ill-conditioned matrices and the integration of stiff ODEs

DOI10.1016/0377-0427(93)90025-7zbMath0798.65081OpenAlexW2029240763MaRDI QIDQ1318436

Lawrence F. Shampine

Publication date: 27 March 1994

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(93)90025-7

zbMATH Keywords

ill-conditioned matricessystems of ordinary differential equationssemi-implicit methodsstiff initial value problemsimplicit linear multistep methodsRosenbrock-methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Multiple scale methods for ordinary differential equations (34E13)

Related Items

Quantum dynamics of a nucleon in the Fermi accelerator, Error autocorrelation in rational approximation and interval estimates. A survey of results

Uses Software

• RODAS
• LINPACK

Cites Work

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• Recent Progress in Extrapolation Methods for Ordinary Differential Equations
• Scaling for Numerical Stability in Gaussian Elimination
• Iterative Refinement Implies Numerical Stability for Gaussian Elimination
• Implementation of Implicit Formulas for the Solution of ODE<scp>s</scp>
• Implementation of Rosenbrock Methods
• Comparing numerical methods for stiff systems of O.D.E:s
• The automatic integration of ordinary differential equations