Multi-step Nyström methods for general second-order initial value problemsy″(t) =f(t,y(t),y′(t))

DOI10.1080/00207160.2018.1464154zbMath1481.65102OpenAlexW2796494805MaRDI QIDQ5031860

Publication date: 16 February 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2018.1464154

zbMATH Keywords

order conditions explicit methods Nyström-series general second-order initial value problems multi-step Nyström methods

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (1)

Adaptive multi-step Runge-Kutta-Nyström methods for general second-order ordinary differential equations

Cites Work

Multi-step hybrid methods for special second-order differential equations \(y^{\prime \prime}(t)=f(t,y(t))\)
ERKN integrators for systems of oscillatory second-order differential equations
General linear methods for \(y^{\prime\prime} = f(y(t))\)
Order conditions for ARKN methods solving oscillatory systems
Multi-step Runge-Kutta-Nyström methods for special second-order initial value problems
Special perturbation theory methods in celestial mechanics. I: Principles for the construction and substantiation of the application
Piecewise-linearized methods for initial-value problems
Obrechkoff methods having additional parameters for general second-order differential equations
On fitted modifications of Runge-Kutta-Nyström pairs
An efficient variable step-size rational Falkner-type method for solving the special second-order IVP
A class of linear multi-step method adapted to general oscillatory second-order initial value problems
Mathematical problems from combustion theory
Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
Order conditions for RKN methods solving general second-order oscillatory systems
Order conditions for general linear Nyström methods
Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
New methods for oscillatory systems based on ARKN methods
High Order Algebraically Stable Multistep Runge–Kutta Methods
Order Properties of Implicit Multivalue Methods for Ordinary Differential Equations
Symmetric Multistip Methods for Periodic Initial Value Problems
On accuracy and unconditional stability of linear multistep methods for second order differential equations
Order conditions for a class of two-step methods for y = f (x, y)
Geometric Numerical Integration
An Algebraic Theory of Integration Methods
Numerical Methods for Ordinary Differential Equations
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