Parallel diagonally implicit Runge-Kutta-Nyström methods

DOI10.1016/0168-9274(92)90009-3zbMath0747.65059OpenAlexW2137106942MaRDI QIDQ1184014

B. P. Sommeijer, P. J. van der Houwen, Nguyen Huu Cong

Publication date: 28 June 1992

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

Full work available at URL: https://ir.cwi.nl/pub/5603

zbMATH Keywords

numerical examplesspectral radiusiterative methodinitial-value problemparallel computersorder reductionsecond order equationslarge Lipschitz constantsdiagonally implicit Runge-Kutta- Nyström method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear ordinary differential equations and systems (34A34) 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 (11)

Optimal three-stage implicit exponentially-fitted RKN methods for solving second-order ODEs ⋮ Note on the performance of direct and indirect Runge-Kutta-Nyström methods ⋮ A parallel DIRK method for stiff initial-value problems ⋮ Exponentially-fitted and trigonometrically-fitted implicit RKN methods for solving \(y^{\prime\prime}=f(t,y)\) ⋮ A fast convergence parallel DIRKN method and its applications to PDEs ⋮ Stein implicit Runge-Kutta methods with high stage order for large-scale ordinary differential equations ⋮ Parallel step-by-step methods ⋮ \(A\)-stable diagonally implicit Runge-Kutta-Nyström methods for parallel computers ⋮ Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations ⋮ Explicit parallel two-step Runge-Kutta-Nyström methods ⋮ Transformation of sine-Gordon solitons in models with variable coefficients and damping

Uses Software

• RODAS

Cites Work

• Stability of collocation-based Runge-Kutta-Nyström methods
• The Tchebychev iteration for nonsymmetric linear systems
• Unconditionally stable methods for second order differential equations
• Parallel iteration of high-order Runge-Kutta methods with stepsize control
• Klassische Runge-Kutta-Nyström-Formeln mit SchrittweitenKontrolle für Differentialgleichungen \(\ddot x= f(t,x)\)
• A Comparison of the Successive Overrelaxation Method and Semi-Iterative Methods Using Chebyshev Polynomials
• Iterated Runge–Kutta Methods on Parallel Computers
• Two-stage and Three-stage Diagonally Implicit Runge-Kutta Nyström Methods of Orders Three and Four
• Stability of collocation methods for the numerical solution ofy″=f (x,y)
• Implementation of Implicit Formulas for the Solution of ODE<scp>s</scp>
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
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