A general framework for the numerical solution of second order odes

DOI10.1016/j.matcom.2014.04.007OpenAlexW2051364687MaRDI QIDQ2228614

Raffaele D'Ambrosio, Beatrice Paternoster

Publication date: 19 February 2021

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2014.04.007

zbMATH Keywords

second-order ordinary differential equationsgeneral linear methodsNyström methodsMEBDF methods

Mathematics Subject Classification ID

Numerical analysis (65-XX) Ordinary differential equations (34-XX)

Related Items (4)

Jacobian-dependent vs Jacobian-free discretizations for nonlinear differential problems ⋮ General Nyström methods in Nordsieck form: error analysis ⋮ Generalized linear multistep methods for ordinary differential equations ⋮ STRONG STABILITY PRESERVING MULTISTAGE INTEGRATION METHODS

Uses Software

• MEBDF
• RODAS

Cites Work

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• A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side
• The integration of stiff initial value problems in ODEs using modified extended backward differentiation formulae
• General linear methods for \(y^{\prime\prime} = f(y(t))\)
• On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae
• Parallel-iterated pseudo two-step Runge-Kutta-Nyström methods for nonstiff second-order IVPs
• Explicit parallel two-step Runge-Kutta-Nyström methods
• \(P\)-stable general Nyström methods for \(y=f(y(t))\)
• Order conditions for general linear Nyström methods
• Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach
• Two Step Runge-Kutta-Nyström Methods for y″ = f(x,y) and P-Stability
• Order conditions for a class of two-step methods for y = f (x, y)
• Numerical Methods for Ordinary Differential Equations

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