Design and implementation of DIRK integrators for stiff systems

DOI10.1016/S0168-9274(03)00012-6zbMath1023.65072MaRDI QIDQ1399153

Roger K. Alexander

Publication date: 30 July 2003

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

zbMATH Keywords

numerical examplesstiff systemsdiagonally implicit Runge-Kutta methodsimplementationstepsize controlembedded methods\(L\)-stabilityDIRK methods

Mathematics Subject Classification ID

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)

Related Items (11)

A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows ⋮ A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations ⋮ Third- and fourth-order ESDIRK methods for stiff and differential-algebraic problems ⋮ Optimization of high-order diagonally-implicit Runge-Kutta methods ⋮ An efficient scheme for the implementation of implicit Runge-Kutta methods ⋮ Diagonally implicit Runge-Kutta methods for stiff problems ⋮ Variable step-size fractional step Runge-Kutta methods for time-dependent partial differential equations ⋮ On the effect of temporal error in high-order simulations of unsteady flows ⋮ Pressure corrected implicit \(\theta \)-schemes for the incompressible Navier-Stokes equations ⋮ Discrete singular convolution for the generalized variable-coefficient Korteweg-de Vries equation ⋮ Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3

Uses Software

• TR-BDF2

Cites Work

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• Error estimators for stiff differential equations
• Local error estimation by doubling
• Starting step size for an ODE solver
• A family of embedded Runge-Kutta formulae
• The approximate Runge-Kutta computational process
• Analysis and implementation of TR-BDF2
• Runge–Kutta Methods and Differential-Algebraic Systems
• Comparing numerical methods for stiff systems of O.D.E:s
• Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations
• Stability of Runge–Kutta Methods for Stiff Ordinary Differential Equations
• ODE solvers and the method of lines
• Efficient Runge-Kutta integrators for index-2 differential algebraic equations
• Implicit Runge-Kutta Processes

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