Parameter optimization for explicit parallel peer two-step methods

DOI10.1016/j.apnum.2008.03.013zbMath1163.65051OpenAlexW2076456542MaRDI QIDQ1007398

Stefan Jebens, Bernhard A. Schmitt, Rüdiger Weiner

Publication date: 20 March 2009

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.03.013

zbMATH Keywords

stabilitylinear programmingnumerical examplesinitial-value problemsparameter optimizationparallel methodsMonte-Carlo simulationExplicit two-step peer methods

Mathematics Subject Classification ID

Monte Carlo methods (65C05) 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 (17)

Order reduction phenomenon for general linear methods ⋮ Two-step peer methods with equation-dependent coefficients ⋮ Superconvergent explicit two-step peer methods ⋮ Parallel start for explicit parallel two-step peer methods ⋮ Two-step peer methods with continuous output ⋮ Functionally fitted explicit two step peer methods ⋮ Exponentially fitted two-step peer methods for oscillatory problems ⋮ On the derivation of explicit two-step peer methods ⋮ Time-accurate and highly-stable explicit peer methods for stiff differential problems ⋮ Linearly implicit peer methods for the compressible Euler equations ⋮ An efficient time-step-based self-adaptive algorithm for predictor-corrector methods of Runge-Kutta type ⋮ Order conditions for general linear methods ⋮ Explicit multi-step peer methods for special second-order differential equations ⋮ Reprint of: Peer methods with improved embedded sensitivities for parameter-dependent ODEs ⋮ Search for efficient general linear methods for ordinary differential equations ⋮ Partially implicit peer methods for the compressible Euler equations ⋮ Adapted explicit two-step peer methods

Cites Work

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• A parallel stiff ODE solver based on MIRKs
• The construction of practical general linear methods
• Rosenbrock-type `peer' two-step methods
• Implicit parallel peer methods for stiff initial value problems
• Explicit general linear methods with inherent Runge--Kutta stability
• Explicit two-step peer methods
• Multi-implicit peer two-step W-methods for parallel time integration
• Solving Ordinary Differential Equations I
• Parallel Two-Step W-Methods with Peer Variables
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations

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