Partitioned adaptive Runge-Kutta methods and their stability

DOI10.1007/BF01389472zbMath0568.65043OpenAlexW2020009818MaRDI QIDQ1060545

Karl Strehmel, Rüdiger Weiner

Publication date: 1984

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

Full work available at URL: https://eudml.org/doc/132969

zbMATH Keywords

numerical examplescontractivitypartitioned systemsnonlinear stiff differential equationspartitioned adaptive 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)

Related Items

B-convergence results for linearly implicit one step methods ⋮ Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems ⋮ A study of B-convergence of linearly implicit Runge-Kutta methods ⋮ On error behaviour of partitioned linearly implicit Runge-Kutta methods for stiff and differential algebraic systems ⋮ Order results for Rosenbrock type methods on classes of stiff equations ⋮ Automatic partitioning in linearly-implicit Runge-Kutta methods

Cites Work

• A semi-implicit mid-point rule for stiff systems of ordinary differential equations
• Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
• Order conditions for numerical methods for partitioned ordinary differential equations
• Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden
• On the stability of semi-implicit methods for ordinary differential equations
• A User’s View of Solving Stiff Ordinary Differential Equations
• Nichtlineare Stabilität adaptiver Runge-Kutta Methoden
• Automatic Partitioning of Stiff Systems and Exploiting the Resulting Structure
• An implementation of singly-implicit Runge-Kutta methods
• Comparing numerical methods for stiff systems of O.D.E:s
• Numerical Integration of Systems of Stiff Ordinary Differential Equations with Special Structure
• A Partially Implicit Method for Large Stiff Systems of ODE<scp>s</scp> with Only Few Equations Introducing Small Time-Constants
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item