Some schemes for the implementation of implicit Runge-Kutta methods

DOI10.1016/0377-0427(93)90276-HzbMath0783.65064MaRDI QIDQ688620

G. J. Cooper, R. Vignesvaran

Publication date: 10 March 1994

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical experimentsspectral radiusconvergence rateimplicit Runge-Kutta methodsiteration matrixmodified Newton iterationlinear iteration schemetwo-stage Gauss method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (11)

Composite symmetric general linear methods (COSY-GLMs) for the long-time integration of reversible Hamiltonian systems ⋮ Iterative schemes for three-stage implicit Runge-Kutta methods ⋮ Improving the efficiency of the iterative schemes for implicit Runge-Kutta methods ⋮ Efficient implementation of second-order implicit Runge-Kutta methods ⋮ Inexact Newton-Type Optimization with Iterated Sensitivities ⋮ Lifted collocation integrators for direct optimal control in ACADO toolkit ⋮ A new one-step method with three intermediate points in a variable step-size mode for stiff differential systems ⋮ Efficient implementation of Gauss collocation and Hamiltonian boundary value methods ⋮ An error embedded method based on generalized Chebyshev polynomials ⋮ Positive and conservative schemes for mass action kinetics ⋮ On the use of parallel processors for implicit Runge-Kutta methods

Cites Work

• Unnamed Item
• Unnamed Item
• A scheme for the implementation of implicit Runge-Kutta methods
• An Iteration Scheme for Implicit Runge—Kutta Methods
• On the Efficient Implementation of Implicit Runge-Kutta Methods
• Efficiency of Methods for Second-Order Problems
• Semiexplicit A-Stable Runge-Kutta Methods
• On the implementation of implicit Runge-Kutta methods
• On a Class of Implicit Runge-Kutta Procedures
• Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations
• An Efficient Solution Process for Implicit Runge–Kutta Methods
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations
• The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
• The implementation of Runge-Kutta implicit processes

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