High-order zero-dissipative Runge-Kutta-Nyström methods

DOI10.1016/S0377-0427(98)00081-8zbMath0937.65083MaRDI QIDQ1298522

Ch. Tsitouras

Publication date: 22 August 1999

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

zbMATH Keywords

numerical resultsperiodic solutionRunge-Kutta-Nyström methodsinterval of periodicitydissipation error

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (5)

A new eighth order exponentially fitted explicit Numerov-type method for solving oscillatory problems ⋮ On fitted modifications of Runge-Kutta-Nyström pairs ⋮ Fitted modifications of Runge–Kutta–Nyström pairs of orders 7(5) for addressing oscillatory problems ⋮ Runge-Kutta-Nyström methods of eighth order for addressing linear inhomogeneous problems ⋮ Optimized Runge-Kutta pairs for problems with oscillating solutions

Cites Work

• A \(P\)-stable eighth-order method for the numerical integration of periodic initial-value problems
• Intervals of periodicity and absolute stability of explicit Nyström methods for y=f(x,y)
• Lack of dissipativity is not symplecticness
• Stabilization of Cowell's method
• A parameter study of explicit Runge-Kutta pairs of orders 6(5)
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Highly Continuous Interpolants for One-Step ODE Solvers and their Application to Runge--Kutta Methods
• A Sixth-order P-stable Symmetric Multistep Method for Periodic Initial-value Problems of Second-order Differential Equations
• High-Order Embedded Runge-Kutta-Nystrom Formulae
• Symmetric Multistip Methods for Periodic Initial Value Problems
• Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
• Cheap Error Estimation for Runge--Kutta Methods
• A General Family of Explicit Runge–Kutta Pairs of Orders $6(5)$
• On Runge-Kutta processes of high order

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