Implications of order reduction for implicit Runge-Kutta methods

DOI10.1007/BF02139474zbMath0757.65089MaRDI QIDQ1200542

W. H. Enright, Craig S. MacDonald

Publication date: 16 January 1993

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

stabilitystiff systemsstiff differential equationslocal errorimplicit Runge-Kutta methodsorder reductionglobal measure of orderobserved orderProthero-Robinson test problemstepsize selection algorithmvariable-step algorithms

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Multiple scale methods for ordinary differential equations (34E13)

Related Items (2)

Time-accurate and highly-stable explicit peer methods for stiff differential problems ⋮ Runge-Kutta research at Toronto

Uses Software

• Maple
• RODAS

Cites Work

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• The numerical solution of differential-algebraic systems by Runge-Kutta methods
• On Order Reduction for Runge–Kutta Methods Applied to Differential/Algebraic Systems and to Stiff Systems of ODEs
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• Order Results for Implicit Runge–Kutta Methods Applied to Differential/Algebraic Systems
• Efficiently Implementable Algebraically Stable Runge–Kutta Methods
• On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• A special stability problem for linear multistep methods

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