Fully parallel Runge-Kutta-Nyström methods for ODEs with oscillating solutions

DOI10.1016/0168-9274(93)90045-SzbMath0782.65090OpenAlexW2066746472MaRDI QIDQ686550

Maria Rosaria Crisci, Elvira Russo, Beatrice Paternoster

Publication date: 10 October 1993

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

Full work available at URL: https://doi.org/10.1016/0168-9274(93)90045-s

zbMATH Keywords

parallel computationoscillatory problemsdispersive order\(P\)-stabilityalgebraic ordermulti stage methodNumerical testsRunge-Kutta- Nyström 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)

Related Items (4)

GPU-acceleration of waveform relaxation methods for large differential systems ⋮ Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials ⋮ A phase-fitted collocation-based Runge-Kutta-Nyström method ⋮ Order bound for a family of parallel Runge-Kutta-Nyström methods through computer algebra

Cites Work

• Unnamed Item
• On the stability of rational approximations to the cosine with only imaginary poles
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Two-stage and Three-stage Diagonally Implicit Runge-Kutta Nyström Methods of Orders Three and Four
• Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• Convergence of Continued Fractions

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