A four-stage index 2 diagonally implicit Runge-Kutta method

DOI10.1016/S0168-9274(01)00090-3zbMath0993.65088OpenAlexW1994850555MaRDI QIDQ5957926

Russell Williams, Ian T. Cameron, Minnie Kerr, Kevin Burrage

Publication date: 13 March 2002

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

Full work available at URL: https://doi.org/10.1016/s0168-9274(01)00090-3

zbMATH Keywords

numerical examplesdifferential algebraic equationsvariable step sizefour-stage, index 2 explicit singly diagonally implicit Runge-Kutta method

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for differential-algebraic equations (65L80) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Cites Work

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• On smoothing and order reduction effects for implicit Runge-Kutta formulae
• Error of Rosenbrock methods for stiff problems studied via differential algebraic equations
• On simplifying assumptions of Runge-Kutta methods for index 2 differential algebraic problems
• Solving Ordinary Differential Equations with Discontinuities
• Solution of Differential—Algebraic Systems Using Diagonally Implicit Runge—Kutta Methods
• Order Properties of Implicit Multivalue Methods for Ordinary Differential Equations
• Differential/Algebraic Equations are not ODE’<scp>s</scp>
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
• Index Reduction in Differential-Algebraic Equations Using Dummy Derivatives

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