General Nyström methods in Nordsieck form: error analysis

DOI10.1016/j.cam.2015.04.041zbMath1329.65150OpenAlexW2093623493MaRDI QIDQ495101

Beatrice Paternoster, Raffaele D'Ambrosio, Giuseppe De Martino

Publication date: 9 September 2015

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.2015.04.041

zbMATH Keywords

error analysisorder conditionssecond order ordinary differential equationsgeneral Nyström methodsmulti-value numerical methods

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items

A fast sine transform accelerated high-order finite difference method for parabolic problems over irregular domains ⋮ Construction of the Nordsieck second derivative methods with RK stability for stiff ODEs ⋮ Collocation methods for Volterra integral and integro-differential equations: a review ⋮ Stability issues for selected stochastic evolutionary problems: a review

Cites Work

• Unnamed Item
• Numerical integration of Hamiltonian problems by G-symplectic methods
• Long-term stability of multi-value methods for ordinary differential equations
• General linear methods for \(y^{\prime\prime} = f(y(t))\)
• A theory for Nyström methods
• Nordsieck representation of DIMSIMs
• A general framework for the numerical solution of second order odes
• \(P\)-stable general Nyström methods for \(y=f(y(t))\)
• G-symplecticity implies conjugate-symplecticity of the underlying one-step method
• Order conditions for general linear Nyström methods
• Error propagation of general linear methods for ordinary differential equations
• On error estimation in general linear methods for stiff ODEs
• On Numerical Integration of Ordinary Differential Equations
• Stability of collocation methods for the numerical solution ofy″=f (x,y)
• Non-linear stability of a general class of differential equation methods
• The Order of Numerical Methods for Ordinary Differential Equations
• Order conditions for a class of two-step methods for y = f (x, y)
• Geometric Numerical Integration
• General linear methods