Rosenbrock-type `peer' two-step methods

DOI10.1016/j.apnum.2004.08.021zbMath1072.65107OpenAlexW2022152008MaRDI QIDQ1772809

Rüdiger Weiner, Helmut Podhaisky, Bernhard A. Schmitt

Publication date: 21 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2004.08.021

zbMATH Keywords

stabilityparallel computationRosenbrock methodsgeneral linear methodsStiff systemsPeer methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (31)

IMEX peer methods for fast-wave-slow-wave problems ⋮ An artificial equation of state based Riemann solver for a discontinuous Galerkin discretization of the incompressible Navier-Stokes equations ⋮ Superconvergent explicit two-step peer methods ⋮ Parallel start for explicit parallel two-step peer methods ⋮ High-order linearly implicit two-step peer schemes for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations ⋮ Two-step peer methods with continuous output ⋮ A class of implicit peer methods for stiff systems ⋮ Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods ⋮ Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods ⋮ Robustness and efficiency of an implicit time-adaptive discontinuous Galerkin solver for unsteady flows ⋮ Exponentially fitted two-step peer methods for oscillatory problems ⋮ On the implementation of explicit two-step peer methods with Runge-Kutta stability ⋮ Extrapolation-based implicit-explicit Peer methods with optimised stability regions ⋮ Explicit two-step peer methods ⋮ Exponential peer methods ⋮ Linearly implicit peer methods for the compressible Euler equations ⋮ Peer methods for the one-dimensional shallow-water equations with CWENO space discretization ⋮ Super-convergent implicit-explicit peer methods with variable step sizes ⋮ Generalized linear multistep methods for ordinary differential equations ⋮ Superconvergent IMEX peer methods ⋮ Local and global error estimation and control within explicit two-step peer triples ⋮ A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems ⋮ A family of \(L\)-stable singly implicit peer methods for solving stiff IVPs ⋮ On error estimation in general linear methods for stiff ODEs ⋮ Linearly-implicit two-step methods and their implementation in Nordsieck form ⋮ Partially implicit peer methods for the compressible Euler equations ⋮ Implicit peer methods for large stiff ODE systems ⋮ High-order linearly implicit two-step peer - finite element methods for time-dependent PDEs ⋮ Parameter optimization for explicit parallel peer two-step methods ⋮ Rosenbrock-Wanner Methods: Construction and Mission ⋮ Two-Step W-Methods

Uses Software

• ROS3P

Cites Work

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• Construction of highly stable two-step W-methods for ordinary differential equations
• Order and effective order
• The construction of practical general linear methods
• Parallel `peer' two-step W-methods and their application to MOL-systems.
• Design, analysis and testing of some parallel two-step W-methods for stiff systems
• Implicit parallel peer methods for stiff initial value problems
• Linearly-implicit two-step methods and their implementation in Nordsieck form
• Multi-implicit peer two-step W-methods for parallel time integration
• Difference Methods for Stiff Ordinary Differential Equations
• Parallel Two-Step W-Methods with Peer Variables
• ROS3P -- An accurate third-order Rosenbrock solver designed for parabolic problems

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