An embedded explicit Runge–Kutta–Nyström method for solving oscillatory problems

DOI10.1088/0031-8949/80/01/015005zbMath1170.65323OpenAlexW2056825689WikidataQ62630616 ScholiaQ62630616MaRDI QIDQ3393673

Mohamed Bin Suleiman, Fudziah Bt. Ismail, Norazak Senu

Publication date: 27 August 2009

Published in: Physica Scripta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0031-8949/80/01/015005

zbMATH Keywords

dissipation dispersion oscillatory solutions second-order differential equations numerical comparisons embedded explicit 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)

Related Items (8)

Embedded explicit Runge-Kutta type methods for directly solving special third order differential equations \(y = f(x, y)\) ⋮ Zero-dissipative semi-implicit hybrid method for solving oscillatory or periodic problems ⋮ One step adapted hybrid second derivative block method for initial value problems with oscillating solutions ⋮ A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems ⋮ Higher order dispersive and dissipative hybrid method for the numerical solution of oscillatory problems ⋮ New \(4(3)\) pairs diagonally implicit Runge-Kutta-Nyström method for periodic IVPs ⋮ A new fourth-order four stage explicit trigonometrically-fitted Runge–Kutta–Nyström method for solving periodic problems ⋮ Adaptive multi-step Runge-Kutta-Nyström methods for general second-order ordinary differential equations

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