Note on the performance of direct and indirect Runge-Kutta-Nyström methods

DOI10.1016/0377-0427(93)90053-EzbMath0774.65047OpenAlexW1989691897MaRDI QIDQ2366439

Nguyen Huu Cong

Publication date: 29 June 1993

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(93)90053-e

zbMATH Keywords

performanceconvergencenumerical examplessecond-order differential equationspredictor-corrector methodsdirect methodsnumerical comparisonimplicit Runge-Kutta-Nyström methods

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) Complexity and performance of numerical algorithms (65Y20)

Related Items

Collocation Runge–Kutta–Nyström methods for solving second-order initial value problems, Parallel iteration of symmetric Runge-Kutta methods for nonstiff initial-value problems, Continuous parallel-iterated RKN-type PC methods for nonstiff IVPs, Explicit symmetric Runge-Kutta-Nyström methods for parallel computers, A general class of explicit pseudo--two-step RKN methods on parallel computers, Fast convergence pirkn-type pc methods with adams-type predictors^∗, \(P\)-stable general Nyström methods for \(y=f(y(t))\), Twostep-by-twostep continuous PIRKN-type PC methods for nonstiff IVPs, Explicit pseudo two-step RKN methods with stepsize control, Explicit parallel two-step Runge-Kutta-Nyström methods, Parallel block pc methods with rkn-type correctors and adams-type predictors^∗, A phase-fitted collocation-based Runge-Kutta-Nyström method, Explicit, high-order Runge-Kutta-Nyström methods for parallel computers, Two-step-by-two-step PIRKN-type PC methods based on Gauss-Legendre collocation points for nonstiff IVPs, RKN-type parallel block PC methods with Lagrange-type predictors, Parallel-iterated pseudo two-step Runge-Kutta-Nyström methods for nonstiff second-order IVPs

Cites Work

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• Klassische Runge-Kutta-Nyström-Formeln mit SchrittweitenKontrolle für Differentialgleichungen \(\ddot x= f(t,x)\)