Approximating Runge-Kutta matrices by triangular matrices

DOI10.1007/BF02510217zbMath0879.65053OpenAlexW2053728561MaRDI QIDQ1359972

Jacques J. B. de Swart, Walter Hoffmann

Publication date: 22 January 1998

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02510217

zbMATH Keywords

stiff systemsRunge-Kutta methodNewton methodtriangular matricesRunge-Kutta matrices

Mathematics Subject Classification ID

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) Multiple scale methods for ordinary differential equations (34E13)

Related Items

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting ⋮ Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs ⋮ Generalized Kronecker product splitting iteration for the solution of implicit Runge-Kutta and boundary value methods ⋮ A parallelizable preconditioner for the iterative solution of implicit Runge-Kutta-type methods ⋮ A splitting preconditioner for the iterative solution of implicit Runge-Kutta and boundary value methods ⋮ CWI contributions to the development of parallel Runge-Kutta methods ⋮ Kronecker product splitting preconditioners for implicit Runge-Kutta discretizations of viscous wave equations

Uses Software

• RODAS

Cites Work

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• An Iteration Scheme for Implicit Runge—Kutta Methods
• Triangularly Implicit Iteration Methods for ODE-IVP Solvers
• Iterated Runge–Kutta Methods on Parallel Computers