Iterative schemes for three-stage implicit Runge-Kutta methods

DOI10.1016/0168-9274(95)00070-BzbMath0885.65086OpenAlexW1969258776MaRDI QIDQ1901533

S. González-Pinto, Luis Rández, Juan I. Montijano

Publication date: 2 April 1998

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

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00070-b

zbMATH Keywords

convergencetest problemsimplicit Runge-Kutta methodsGauss methodNewton schemeRadau IIA methodslarge stiff problem

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)

Related Items (19)

Efficient iterations for Gauss methods on second-order problems ⋮ Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs ⋮ An iterated Radau method for time-dependent PDEs ⋮ On the numerical solution of stiff IVPs by Lobatto IIIA Runge-Kutta methods ⋮ Starting algorithms for IRK methods ⋮ Improving the efficiency of the iterative schemes for implicit Runge-Kutta methods ⋮ Brownian motion and thermophoresis behavior on micro-polar nano-fluid -- a numerical outlook ⋮ Efficient delay and parameter estimation for nonlinear systems based on lifted IRK integrators with inexact Jacobians ⋮ Inexact Newton-Type Optimization with Iterated Sensitivities ⋮ Lifted collocation integrators for direct optimal control in ACADO toolkit ⋮ Stabilized starting algorithms for collocation Runge-Kutta methods. ⋮ Performance of Gauss implicit Runge-Kutta methods on separable Hamiltonian systems. ⋮ A parallelizable preconditioner for the iterative solution of implicit Runge-Kutta-type methods ⋮ Efficient implementation of Radau collocation methods ⋮ A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems ⋮ Speeding up Newton-type iterations for stiff problems ⋮ Implementation of high-order implicit Runge-Kutta methods ⋮ Variable-order starting algorithms for implicit Runge-Kutta methods on stiff problems ⋮ AMF-Runge-Kutta formulas and error estimates for the time integration of advection diffusion reaction PDEs

Uses Software

• NSDTST
• STDTST

Cites Work

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• Some schemes for the implementation of implicit Runge-Kutta methods
• A scheme for the implementation of implicit Runge-Kutta methods
• Iterative schemes for Gauss methods
• Some linear stability results for iterative schemes for implicit Runge-Kutta methods
• An Iteration Scheme for Implicit Runge—Kutta Methods
• Second derivative methods applied to implicit first- and second-order systems
• Efficiency of Methods for Second-Order Problems
• Implementation of Implicit Formulas for the Solution of ODE<scp>s</scp>
• On the implementation of implicit Runge-Kutta methods
• An Efficient Solution Process for Implicit Runge–Kutta Methods
• Blended Linear Multistep Methods
• Two FORTRAN packages for assessing initial value methods

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