Numerical experiments with some explicit pseudo two-step RK methods on a shared memory computer

DOI10.1016/S0898-1221(98)00121-7zbMath0932.65085MaRDI QIDQ1806457

Rüdiger Weiner, Helmut Podhaisky, Nguyen Huu Cong

Publication date: 15 March 2000

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

performancestabilitynumerical experimentsparallel computationstepsize controlpseudo two-step 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) 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) Complexity and performance of numerical algorithms (65Y20) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Collocation Runge–Kutta–Nyström methods for solving second-order initial value problems ⋮ Parallel predictor-corrector iteration of pseudo two-step RK methods for nonstiff IVPs ⋮ Parallel-iterated pseudo two-step Runge-Kutta methods with step size control ⋮ On the derivation of explicit two-step peer methods ⋮ Explicit two-step peer methods ⋮ Two-step-by-two-step PIRK-type PC methods based on Gauss-Legendre collocation points ⋮ Improved parallel-iterated pseudo two-step RK methods for nonstiff IVPs ⋮ Twostep-by-twostep PIRK-type PC methods with continuous output formulas ⋮ Functionally fitted explicit pseudo two-step Runge-Kutta methods ⋮ Explicit pseudo two-step RKN methods with stepsize control ⋮ Parallel-Iterated RK-Type PC Methods With Continuous Output Formulas * This work was partly supported by N.R.P.F.S. ⋮ Parallel two-step ROW-methods for stiff delay differential equations ⋮ Continuous variable stepsize explicit pseudo two-step RK methods ⋮ Design, analysis and testing of some parallel two-step W-methods for stiff systems

Uses Software

• ROWMAP

Cites Work

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• Parallel methods for initial value problems
• Efficient block predictor-corrector methods with a small number of corrections
• Continuous variable stepsize explicit pseudo two-step RK methods
• Parallel block predictor-corrector methods of Runge-Kutta type
• On the implementation of parallel iterated Runge-Kutta methods on a transputer network
• Parallel iteration of symmetric Runge-Kutta methods for nonstiff initial-value problems
• Implementing an ODE code on distributed memory computers
• Parallel iterated methods based on multistep Runge-Kutta methods of Radau type
• ROWMAP -- a ROW-code with Krylov techniques for large stiff ODEs
• Parallel iteration of high-order Runge-Kutta methods with stepsize control
• A class of explicit parallel two-step Runge-Kutta methods
• Solving Ordinary Differential Equations I
• Block Runge-Kutta Methods on Parallel Computers
• The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
• Explicit pseudo two-step runge-kutta methods for parallel computers^∗
• Comparing Numerical Methods for Ordinary Differential Equations