Order and effective order

DOI10.1016/S0168-9274(98)00043-9zbMath0927.65095MaRDI QIDQ1294505

John C. Butcher

Publication date: 25 November 1999

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

stiff systemsRunge-Kutta methodseffective order

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (5)

Superconvergent IMEX peer methods ⋮ Rosenbrock-type `peer' two-step methods ⋮ Implicit peer methods for large stiff ODE systems ⋮ Effective order of partitioned Runge-Kutta methods ⋮ Symplectic effective order numerical methods for separable Hamiltonian systems

Uses Software

• DESIRE
• DESI

Cites Work

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• DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods
• A generalization of singly-implicit Runge-Kutta methods
• The effective order of singly-implicit Runge-Kutta methods
• Solving Ordinary Differential Equations I
• Towards Efficient Runge–Kutta Methods for Stiff Systems
• DESI methods for stiff initial-value problems
• Local Estimation of the Global Discretization Error
• An algebraic approach to Runge-Kutta methods
• The number of conditions for a Runge-Kutta method to have effective order \(p\)

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