A class of linear multi-step method adapted to general oscillatory second-order initial value problems

DOI10.1007/s12190-017-1087-2zbMath1486.65076OpenAlexW2587964632MaRDI QIDQ1743385

Ming Lu, Xianfen Wang, Jiyong Li

Publication date: 13 April 2018

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

Full work available at URL: https://doi.org/10.1007/s12190-017-1087-2

zbMATH Keywords

oscillatory systemslocal truncation error\(\phi\)-functionsadapted methodsgeneral oscillatory second-order initial value problems

Mathematics Subject Classification ID

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

Multi-step Nyström methods for general second-order initial value problemsy″(t) =f(t,y(t),y′(t)), Multi-step hybrid methods adapted to the numerical integration of oscillatory second-order systems

Cites Work

• A note on variable step-size formulation of a Simpson's-type second derivative block method for solving stiff systems
• A unified approach for the development of \(k\)-step block Falkner-type methods for solving general second-order initial-value problems in ODEs
• ERKN integrators for systems of oscillatory second-order differential equations
• Multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems
• Solving second order initial value problems by a hybrid multistep method without predictors
• Order conditions for ARKN methods solving oscillatory systems
• Extended RKN-type methods for numerical integration of perturbed oscillators
• Variable-stepsize Chebyshev-type methods for the integration of second-order I.V.P.'s
• An adapted explicit hybrid method of Numerov-type for the numerical integration of perturbed oscillators
• Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations
• Trigonometrically-fitted ARKN methods for perturbed oscillators
• Special perturbation theory methods in celestial mechanics. I: Principles for the construction and substantiation of the application
• Pseudo-symplectic Runge-Kutta methods
• A numerical method for the integration of perturbed linear problems
• High order adaptive methods of Nyström-Cowell type
• Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.
• Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
• Trigonometrically fitted block Numerov type method for \(y = f(x, y, y')\)
• Order conditions for RKN methods solving general second-order oscillatory systems
• New methods for oscillatory systems based on ARKN methods
• Computing matrix functions
• Accurate Numerical Integration of Perturbed Oscillatory Systems in Two Frequencies
• Geometric Numerical Integration
• Numerical Methods for Ordinary Differential Equations
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