On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods

DOI10.1016/S0377-0427(97)00183-0zbMath0898.65047OpenAlexW2149511422MaRDI QIDQ1379027

T. Van Hecke, H. E. De Meyer, Guido Vanden Berghe, Marnix van Daele

Publication date: 1997

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(97)00183-0

zbMATH Keywords

P-stabilityimplicit Runge-Kutta-Nyström methodsmono-implicit Runge-Kutta methods

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

Related Items (8)

Erratum to ``On the generation of \(P\)-stable exponentially fitted Runga-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods ⋮ Generalized Laguerre pseudospectral method based Laguerre interpolation ⋮ Recent advances in linear analysis of convergence for splittings for solving ODE problems ⋮ Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations ⋮ Laguerre-Gauss collocation method for initial value problems of second order ODEs ⋮ On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods ⋮ On the generation of \(P\)-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods. ⋮ Mono-implicit Runge-Kutta formulae for the numerical solution of second order nonlinear two-point boundary value problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A mono-implicit Runge-Kutta-Nyström modification of the Numerov method
• Efficient P-stable methods for periodic initial value problems
• Stability of collocation-based Runge-Kutta-Nyström methods
• An \(A\)-stable extended trapezoidal rule for the integration of ordinary differential equations
• Relationships among some classes of implicit Runge-Kutta methods and their stability functions
• Efficient fourth order P-stable formulae
• Efficient sixth order methods for nonlinear oscillation problems
• High order P-stable formulae for the numerical integration of periodic initial value problems
• Multistride \(L\)-stable fourth-order methods for the numerical solution of ODEs
• A class of stabilized extended one-step methods for the numerical solution of ODEs
• Extended double-stride \(L\)-stable methods for the numerical solution of ODEs
• A general theory of stabilized extended one-step methods for odes
• Extended one-step methods for the numerical solution of ordinary differential equations
• High-accuracy P-stable Methods for y^″ = f(t, y)
• Efficient higher order implicit one-step methods for integration of stiff differential equations
• Mono-implicit Runge—Kutta Formulae for the Numerical Integration of Stiff Differential Systems
• Symmetric Multistip Methods for Periodic Initial Value Problems
• Order Results for Mono-Implicit Runge–Kutta Methods

This page was built for publication: On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods