Parallel Runge-Kutta methods with real eigenvalues

DOI10.1016/0168-9274(93)90051-RzbMath0782.65093MaRDI QIDQ686557

Bojan Orel

Publication date: 10 October 1993

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

zbMATH Keywords

stabilityparallel computationcollocationimplicit Runge-Kutta methodslocal error estimatePadé tableau

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) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (8)

The solution of implicit differential equations on parallel computers ⋮ Highly stable parallel Runge-Kutta methods ⋮ Experiences with sparse matrix solvers in parallel ODE software ⋮ A parallelizable preconditioner for the iterative solution of implicit Runge-Kutta-type methods ⋮ CWI contributions to the development of parallel Runge-Kutta methods ⋮ Analysis approximate factorization in iteration methods ⋮ Mono-implicit Runge-Kutta schemes for the parallel solution of initial value ODEs ⋮ Parallel Adams methods

Cites Work

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• Relationships among some classes of implicit Runge-Kutta methods and their stability functions
• Real pole approximations to the exponential function
• On the Theory of Parallel Runge—Kutta Methods
• A Transformed implicit Runge-Kutta Method
• Mono-implicit Runge—Kutta Formulae for the Numerical Integration of Stiff Differential Systems
• On the implementation of implicit Runge-Kutta methods
• A special family of Runge-Kutta methods for solving stiff differential equations
• Restricted Padé Approximations to the Exponential Function
• Implicit Runge-Kutta Processes

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