On the Efficient Implementation of Implicit Runge-Kutta Methods

DOI10.2307/2006296zbMath0414.65043OpenAlexW4243235237MaRDI QIDQ3049766

James M. Varah

Publication date: 1979

Full work available at URL: https://doi.org/10.2307/2006296

zbMATH Keywords

ordinary differential equationinitial value problemnumerical solutionimplicit Runge-Kutta methods\(A\)-stable methods

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (13)

Efficient classes of Runge-Kutta methods for two-point boundary value problems ⋮ Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs ⋮ The Modified Newton Method in the Solution of Stiff Ordinary Differential Equations ⋮ On the Implementation of Singly Implicit Runge-Kutta Methods ⋮ Unnamed Item ⋮ A method for constructing generalized Runge-Kutta methods ⋮ \(A\)-stability of Runge-Kutta methods for systems with additive noise ⋮ Some schemes for the implementation of implicit Runge-Kutta methods ⋮ An efficient implementation scheme of the simplified Newton iteration for block systems of nonlinear equations ⋮ An implementation of singly-implicit Runge-Kutta methods ⋮ Recent advances in methods for numerical solution of O.D.E. initial value problems ⋮ Diagonally implicit Runge-Kutta formulae for the numerical integration of nonlinear two-point boundary value problems ⋮ A scheme for the implementation of implicit Runge-Kutta methods

Cites Work

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• A Transformed implicit Runge-Kutta Method
• On the implementation of implicit Runge-Kutta methods
• Attainable order of rational approximations to the exponential function with only real poles
• An Efficient Solution Process for Implicit Runge–Kutta Methods
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• A special family of Runge-Kutta methods for solving stiff differential equations
• Stiffly Stable Linear Multistep Methods of Extended Order
• Second Derivative Multistep Methods for Stiff Ordinary Differential Equations
• A-stable Runge-Kutta processes
• The implementation of Runge-Kutta implicit processes
• Implicit Runge-Kutta Processes

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