Towards Efficient Runge–Kutta Methods for Stiff Systems

DOI10.1137/0727044zbMath0702.65072OpenAlexW1972050171MaRDI QIDQ3481182

Jeff R. Cash, John C. Butcher

Publication date: 1990

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0727044

zbMATH Keywords

stiff systemsdiagonally implicit Runge-Kutta methodsL-stabilitysingly implicit Runge-Kutta methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

The NUMOL solution of time-dependent PDEs using DESI Runge-Kutta formulae ⋮ Runge–Kutta Methods for Ordinary Differential Equations ⋮ A generalization of singly-implicit Runge-Kutta methods ⋮ The efficiency of singly-implicit Runge-Kutta methods for stiff differential equations ⋮ Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems ⋮ Numerical strategies for the system of first-order IVPS using the RK–Butcher algorithm ⋮ Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation ⋮ Local error estimation for singly-implicit formulas by two-step Runge- Kutta methods ⋮ Efficient Runge-Kutta integrators for index-2 differential algebraic equations ⋮ Applications of doubly companion matrices ⋮ Adaptive nested implicit Runge-Kutta formulas of Gauss type ⋮ Optimal control of singular systems using the rk–butcher algorithm ⋮ Order and effective order ⋮ The Nørsett time integration methodology for finite element transient analysis