Symbolic derivation of order conditions for hybrid Numerov-type methods solving \(y^{\prime\prime} =f(x,y)\)

DOI10.1016/j.cam.2007.09.017zbMath1143.65055OpenAlexW2091245503MaRDI QIDQ932743

Ch. Tsitouras, Ioannis Th. Famelis

Publication date: 11 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.cam.2007.09.017

zbMATH Keywords

order conditionsinteger partitionstruncation errorrooted treesMATHEMATICA\(^{\circledR}\)Numerov-type methods

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Packaged methods for numerical algorithms (65Y15) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (12)

On ninth order, explicit Numerov-type methods with constant coefficients ⋮ A new eighth order exponentially fitted explicit Numerov-type method for solving oscillatory problems ⋮ Economical handling of Runge-Kutta-Nyström step rejection ⋮ Evolutionary derivation of sixth-order P-stable SDIRKN methods for the solution of PDEs with the method of lines ⋮ On high order Runge-Kutta-Nyström pairs ⋮ 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 \(y^{\prime \prime}=f(x,y)\) ⋮ NUMEROV-TYPE METHODS FOR OSCILLATORY LINEAR INITIAL VALUE PROBLEMS

Uses Software

• Mathematica
• Runge-Kutta Order Conditions
• rktree
• butcher

Cites Work

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