New family for Runge‐Kutta‐Nyström pairs of orders 6(4) with coefficients trained to address oscillatory problems

DOI10.1002/mma.8273zbMath1527.65052OpenAlexW4226479082MaRDI QIDQ6066293

Unnamed Author, Ch. Tsitouras, Vladislav N. Kovalnogov, Theodore E. Simos, M. I. Kornilova, Unnamed Author

Publication date: 12 December 2023

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.8273

zbMATH Keywords

initial value problemnumerical solutionperiodic problemsRunge-Kutta-Nyström

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (1)

Super-stable spline-in-tension numerical method of order three(four) for the second order nonlinear IVPs

Cites Work

• On the numerical integration of second-order initial value problems with a periodic forcing function
• Differential evolution -- a simple and efficient heuristic for global optimization over continuous spaces
• A new optimized non-FSAL embedded Runge-Kutta-Nyström algorithm of orders 6 and 4 in six stages
• Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs
• Explicit, ninth order, two step methods for solving inhomogeneous linear problems \(x(t)= \Lambda x(t)+f(t)\)
• Families of Runge-Kutta-Nystrom Formulae
• Some Practical Runge-Kutta Formulas
• Eine Runge-Kutta-Nyström-Formel 9-ter Ordnung mit Schrittweitenkontrolle für Differentialgleichungenx =f(t, x)
• High Phase-Lag-Order Runge--Kutta and Nyström Pairs
• On Runge-Kutta processes of high order
• Numerical Methods for Ordinary Differential Equations

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