Analysis of parallel diagonally implicit iteration of Runge-Kutta methods

DOI10.1016/0168-9274(93)90047-UzbMath0787.65054MaRDI QIDQ686552

P. J. van der Houwen, B. P. Sommeijer

Publication date: 10 October 1993

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

zbMATH Keywords

stabilityconvergencestiff equationsRunge-Kutta methods\(A\)-stable\(L\)-stablebackward differentiationparallel diagonally implicit iterationPDIRK 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)

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A parallel DIRK method for stiff initial-value problems, Step-parallel algorithms for stiff initial value problems, Numerical results for a parallel linearly-implicit Runge-Kutta method, Two three-parallel and three-processor SDIRK methods for stiff initial-value problems, Experiences with sparse matrix solvers in parallel ODE software, Parallelizing spectral deferred corrections across the method, Applications of time parallelization, Parallel step-by-step methods, Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations, A parallel diagonally iterated RK method for convection-diffusion and stiff problems, CWI contributions to the development of parallel Runge-Kutta methods, PARALLEL SOLUTION METHODS AND PRECONDITIONERS FOR EVOLUTION EQUATIONS, A semi-implicit numerical scheme for reacting flow. II: Stiff, operator-split formulation, Partitioned Krylov subspace iteration in implicit Runge-Kutta methods

Uses Software

• RODAS

Cites Work

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• Implicit Runge-Kutta Processes