General linear methods for \(y^{\prime\prime} = f(y(t))\)

DOI10.1007/s11075-012-9637-zzbMath1275.65039OpenAlexW2123271762MaRDI QIDQ695621

Beatrice Paternoster, Raffaele D'Ambrosio, Elena Esposito

Publication date: 21 December 2012

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-012-9637-z

zbMATH Keywords

convergence analysisconsistencyinitial value problemsecond-order ordinary differential equationsgeneral linear methodszero-stability

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (23)

Modified multi-step Nyström methods for oscillatory general second-order initial value problems ⋮ Multi-step Nyström methods for general second-order initial value problemsy″(t) =f(t,y(t),y′(t)) ⋮ Multi-step hybrid methods for special second-order differential equations \(y^{\prime \prime}(t)=f(t,y(t))\) ⋮ Trigonometrically fitted multi-step RKN methods for second-order oscillatory initial value problems ⋮ Variable stepsize multivalue collocation methods ⋮ Numerical integration of Hamiltonian problems by G-symplectic methods ⋮ Multivalue collocation methods free from order reduction ⋮ Order conditions for general linear Nyström methods ⋮ A general framework for the numerical solution of second order odes ⋮ Rosenbrock-type methods applied to discontinuous differential systems ⋮ An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown ⋮ General Nyström methods in Nordsieck form: error analysis ⋮ Construction of the Nordsieck second derivative methods with RK stability for stiff ODEs ⋮ \(P\)-stable general Nyström methods for \(y=f(y(t))\) ⋮ Exponentially fitted singly diagonally implicit Runge-Kutta methods ⋮ Multi-step hybrid methods adapted to the numerical integration of oscillatory second-order systems ⋮ Nearly conservative multivalue methods with extended bounded parasitism ⋮ Multivalue second derivative collocation methods ⋮ STRONG STABILITY PRESERVING MULTISTAGE INTEGRATION METHODS ⋮ Revised exponentially fitted Runge-Kutta-Nyström methods ⋮ Multi-value Numerical Methods for Hamiltonian Systems ⋮ Trigonometrically fitted multi-step hybrid methods for oscillatory special second-order initial value problems ⋮ A symmetric nearly preserving general linear method for Hamiltonian problems

Uses Software

• RODAS

Cites Work

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• Two-step hybrid collocation methods for \(y^{\prime\prime} = f(x,y)\)
• Explicit general linear methods with inherent Runge--Kutta stability
• Non-linear stability of a general class of differential equation methods
• 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)
• Runge-Kutta-Nyström Stability for a Class of General Linear Methods for yʺ = f(x,y)
• Numerical Methods for Ordinary Differential Equations

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