Stabilized starting algorithms for collocation Runge-Kutta methods.

DOI10.1016/S0898-1221(03)80027-5zbMath1036.65062MaRDI QIDQ1416397

S. Pérez-Rodríguez, S. González-Pinto, Juan I. Montijano

Publication date: 14 December 2003

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

numerical resultsstabilizationNewton-type iterationsimplicit Runge-Kutta methodsstiff initial value problemsstarting algorithmscollocation Runge-Kutta methods

Mathematics Subject Classification ID

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) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (4)

Starting algorithms for a class of RK methods for index-2 DAEs ⋮ A 17th-order radau IIA method for package \texttt{RADAU}. Applications in mechanical systems ⋮ Stage value predictors for additive and partitioned Runge-Kutta methods ⋮ Variable-order starting algorithms for implicit Runge-Kutta methods on stiff problems

Cites Work

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• On the starting algorithms for fully implicit Runge-Kutta methods
• Iterative schemes for three-stage implicit Runge-Kutta methods
• Comparing numerical methods for stiff systems of O.D.E:s
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Stage Value Predictors and Efficient Newton Iterations in Implicit Runge--Kutta Methods

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