Implicit peer methods for large stiff ODE systems

DOI10.1007/s12190-011-0485-0zbMath1295.65079OpenAlexW1974196958MaRDI QIDQ2511024

Rüdiger Weiner, Bernhard A. Schmitt, Steffen Beck, Helmut Podhaisky

Publication date: 5 August 2014

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-011-0485-0

zbMATH Keywords

numerical examplesdiffusion equationsemidiscretizationKrylov subspace methodzero-stabilityinexact Newton methodArnoldi methodfull orthogonalization methodlarge stiff systemsimplicit two-step peer method

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for stiff equations (65L04)

Related Items (23)

IMEX peer methods for fast-wave-slow-wave problems ⋮ Discrete adjoint implicit peer methods in optimal control ⋮ Two-step peer methods with continuous output ⋮ Efficient A-stable peer two-step methods ⋮ Space-time adaptive linearly implicit peer methods for parabolic problems ⋮ A class of implicit peer methods for stiff systems ⋮ New third- and fourth-order singly diagonally implicit two-step peer triples with local and global error controls for solving stiff ordinary differential equations ⋮ 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 ⋮ Extrapolation-based super-convergent implicit-explicit peer methods with A-stable implicit part ⋮ Super-convergent implicit-explicit peer methods with variable step sizes ⋮ Improving the stochastic direct simulation method with applications to evolution partial differential equations ⋮ Order conditions for general linear methods ⋮ Superconvergent IMEX peer methods ⋮ Reprint of: Peer methods with improved embedded sensitivities for parameter-dependent ODEs ⋮ Stability and consistency of discrete adjoint implicit peer methods ⋮ Search for efficient general linear methods for ordinary differential equations ⋮ 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 ⋮ Application of approximate matrix factorization to high order linearly implicit Runge-Kutta methods ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations ⋮ Accurate implicit-explicit general linear methods with inherent Runge-Kutta stability

Uses Software

• Matlab
• ROWMAP

Cites Work

• Unnamed Item
• On the derivation of explicit two-step peer methods
• Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
• Order and effective order
• ROWMAP -- a ROW-code with Krylov techniques for large stiff ODEs
• Rosenbrock-type `peer' two-step methods
• Implicit parallel peer methods for stiff initial value problems
• Superconvergent explicit two-step peer methods
• Multi-implicit peer two-step W-methods for parallel time integration
• Variable-Stepsize Interpolating Explicit Parallel Peer Methods with Inherent Global Error Control
• Analysis of Fixed-Stepsize Methods
• Exponential Integrators for Large Systems of Differential Equations
• Parallel Two-Step W-Methods with Peer Variables

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