Convergence aspects of step-parallel iteration of Runge-Kutta methods

DOI10.1016/0168-9274(95)00063-ZzbMath0837.65076OpenAlexW2142448970MaRDI QIDQ1902089

W. A. van der Veen, P. J. van der Houwen, Jacques J. B. de Swart

Publication date: 7 January 1996

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

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00063-z

zbMATH Keywords

convergenceparallel computationimplicit Runge-Kutta methodsiteration methodstest equationparallelism across stepsRadau IIA

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) 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

Step-parallel algorithms for stiff initial value problems ⋮ Feedforward neural nets as discretization schemes for ODEs and DAEs ⋮ CWI contributions to the development of parallel Runge-Kutta methods

Uses Software

• RODAS

Cites Work

• Parallel ODE-solvers with stepsize control
• Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
• Parallelism across the steps in iterated Runge-Kutta methods for stiff initial value problems
• Parallel iteration across the steps of high-order Runge-Kutta methods for nonstiff initial value problems
• Step-parallel algorithms for stiff initial value problems
• Iterated Runge–Kutta Methods on Parallel Computers
• The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
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