Convergence of general linear methods on differential-algebraic systems of index 3

DOI10.1007/BF02510221zbMath0879.65054OpenAlexW2076091053MaRDI QIDQ1359976

Stefan Schneider

Publication date: 22 January 1998

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02510221

zbMATH Keywords

performancestabilityconvergencebackward differentiation formula methodsdifferential algebraic equationsRunge-Kutta methodslinear multistep methodsindex 3 problemmultistep three-stage Radau method

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Uses Software

• DASSL
• RODAS

Cites Work

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• Numerical experiments with a multistep Radau method
• Stability of multistep-methods on variable grids
• The stability function for multistep collocation methods
• Integration of stiff mechanical systems by Runge-Kutta methods
• Convergence results for general linear methods on singular perturbation problems
• Convergence results for multistep Runge-Kutta methods on stiff mechanical systems
• The numerical solution of differential-algebraic systems by Runge-Kutta methods
• Local error estimation for multistep collocation methods
• The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods
• An implementation of singly-implicit Runge-Kutta methods
• An Efficient Solution Process for Implicit Runge–Kutta Methods

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