Quasi stage order conditions for SDIRK methods

DOI10.1016/S0168-9274(01)00142-8zbMath0998.65071MaRDI QIDQ1612448

Frank Cameron, Robert Piché, Mikko Palmroth

Publication date: 22 August 2002

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

zbMATH Keywords

numerical testsstiff systemsRunge-Kutta methoddifferential algebraic equationserror estimatordiagonally implicit RK methodstage order condition

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) 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) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for differential-algebraic equations (65L80)

Related Items (9)

GIP integrators for matrix Riccati differential equations ⋮ Third- and fourth-order ESDIRK methods for stiff and differential-algebraic problems ⋮ Optimization of high-order diagonally-implicit Runge-Kutta methods ⋮ Diagonally implicit Runge-Kutta methods for stiff problems ⋮ An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods ⋮ A Lyapunov and Sacker-Sell spectral stability theory for one-step methods ⋮ The Prothero and Robinson example: convergence studies for Runge-Kutta and Rosenbrock-Wanner methods ⋮ Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3 ⋮ An analysis of the Prothero-Robinson example for constructing new adaptive ESDIRK methods of order 3 and 4

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Local error control in SDIRK-methods
• A class of low order DIRK methods for a class of DAEs
• The numerical solution of differential-algebraic systems by Runge-Kutta methods
• Convergence of a class of Runge-Kutta methods for differential-algebraic systems of index 2
• Runge-Kutta Methods Applied to Fully Implicit Differential-Algebraic Equations of Index 1
• Order Results for Implicit Runge–Kutta Methods Applied to Differential/Algebraic Systems
• Semiexplicit A-Stable Runge-Kutta Methods
• On Improving the Convergence of Radau IIA Methods Applied to Index 2 DAEs
• ODE solvers and the method of lines
• Efficient Runge-Kutta integrators for index-2 differential algebraic equations
• High-order explicit Runge-Kutta pairs with low stage order

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