Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems

DOI10.1007/BF01395815zbMath0655.65095MaRDI QIDQ1109532

Rüdiger Weiner, Jürgen Bruder, Karl Strehmel

Publication date: 1988

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133257

zbMATH Keywords

stiff systemsButcher seriesorder conditionsmatrix exponentialscomparisonsstepsize selectionstiffness detectionnonstiff systemsadaptive Runge-Kutta methodsexplicit s-stage Runge-Kutta method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

B-convergence results for linearly implicit one step methods, Partitioning ordinary differential equations using Runge-Kutta methods, Varying the componentwise order of the multistep methods in solving ODEs and its absolute stability, Numerical results for a parallel linearly-implicit Runge-Kutta method, Singly-implicit Runge-Kutta methods for retarded and ordinary differential equations, Reciprocal polynomial extrapolation vs Richardson extrapolation for singular perturbed boundary problems, Partitioning methods for reaction-diffusion problems, Efficient variable stiffness methods for cooling of hot-rolled steel sections., Linearly-implicit Runge-Kutta methods based on implicit Runge-Kutta methods

Uses Software

• ODEPACK

Cites Work

• Partitioned Runge-Kutta methods with stiffness detection and stepsize control
• D-stability and Kaps-Rentrop-methods
• Rational Runge-Kutta methods are not suitable for stiff systems of ODEs
• Run time estimation of the spectral radius of Jacobians
• Partitioned adaptive Runge-Kutta methods and their stability
• A reliable Rosenbrock integrator for stiff differential equations
• Order conditions for numerical methods for partitioned ordinary differential equations
• Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden
• On the Butcher group and general multi-value methods
• C-polynomials for rational approximation to the exponential function
• Numerical solution of ordinary differential equations
• Type-Insensitive ODE Codes Based on Extrapolation Methods
• Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations
• D-Stability
• Implementation of Rosenbrock Methods
• Comparing numerical methods for stiff systems of O.D.E:s
• A Partially Implicit Method for Large Stiff Systems of ODE<scp>s</scp> with Only Few Equations Introducing Small Time-Constants
• Comparing Numerical Methods for Ordinary Differential Equations
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