Symbolic derivation of Runge-Kutta-Nyström order conditions

DOI10.1007/s10910-009-9560-2zbMath1185.65127OpenAlexW2149054634MaRDI QIDQ1037494

Ch. Tsitouras, Ioannis Th. Famelis

Publication date: 16 November 2009

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-009-9560-2

zbMATH Keywords

algorithmsnumerical examplesRunge-Kutta-Nyström methodsMathematicaorder conditionsinteger partitionstruncation errorrooted trees

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) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (15)

On ninth order, explicit Numerov-type methods with constant coefficients ⋮ On fitted modifications of Runge-Kutta-Nyström pairs ⋮ Explicit Runge-Kutta-Nyström methods for the numerical solution of second order linear inhomogeneous IVPs ⋮ Evolutionary derivation of sixth-order P-stable SDIRKN methods for the solution of PDEs with the method of lines ⋮ Fitted modifications of Runge–Kutta–Nyström pairs of orders 7(5) for addressing oscillatory problems ⋮ On high order Runge-Kutta-Nyström pairs ⋮ Symbolic derivation of Runge-Kutta-Nyström type order conditions and methods for solving \(y' = f(x, y)\) ⋮ On modifications of Runge-Kutta-Nyström methods for solving \(y^{(4)} = f(x, y)\) ⋮ Explicit, ninth order, two step methods for solving inhomogeneous linear problems \(x(t)= \Lambda x(t)+f(t)\) ⋮ Explicit, eighth-order, four-step methods for solving \(y^{\prime\prime}=f(x, y)\) ⋮ Explicit Runge-Kutta methods for starting integration of Lane-Emden problem ⋮ Hybrid Numerov-type methods with coefficients trained to perform better on classical orbits ⋮ Trigonometric-fitted explicit Numerov-type method with vanishing phase-lag and its first and second derivatives ⋮ Eighth order, phase-fitted, six-step methods for solving \(y^{\prime \prime}=f(x,y)\) ⋮ Runge-Kutta-Nyström methods of eighth order for addressing linear inhomogeneous problems

Uses Software

• Mathematica
• Runge-Kutta Order Conditions
• butcher

Cites Work

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