A scheme for the implementation of implicit Runge-Kutta methods

DOI10.1007/BF02238800zbMath0726.65083OpenAlexW1607052731MaRDI QIDQ804250

R. Vignesvaran, G. J. Cooper

Publication date: 1990

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02238800

zbMATH Keywords

convergence ratesnonlinear systemnumerical examplesiterative schemeimplicit Runge-Kutta methodstiff equationsLU-decompositionimplementationGauss methods

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) 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) Multiple scale methods for ordinary differential equations (34E13)

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Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs ⋮ Iterative schemes for three-stage implicit Runge-Kutta methods ⋮ Some linear stability results for iterative schemes for implicit Runge-Kutta methods ⋮ On the numerical solution of stiff IVPs by Lobatto IIIA Runge-Kutta methods ⋮ Improving the efficiency of the iterative schemes for implicit Runge-Kutta methods ⋮ A parallelizable preconditioner for the iterative solution of implicit Runge-Kutta-type methods ⋮ Efficient implementation of Radau collocation methods ⋮ Theoretically optimal inexact spectral deferred correction methods ⋮ Symplectic Runge-Kutta and related methods: Recent results ⋮ Some schemes for the implementation of implicit Runge-Kutta methods ⋮ Speeding up Newton-type iterations for stiff problems ⋮ Implementation of high-order implicit Runge-Kutta methods ⋮ On the use of parallel processors for implicit Runge-Kutta methods ⋮ Variable-order starting algorithms for implicit Runge-Kutta methods on stiff problems ⋮ Iterative schemes for Gauss methods

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• An Efficient Solution Process for Implicit Runge–Kutta Methods
• The implementation of Runge-Kutta implicit processes