Gauss-Runge-Kutta-Nyström methods

DOI10.1007/BF02510913zbMath0904.65076MaRDI QIDQ1387233

Christopher Burnton, Rudolf Scherer

Publication date: 19 January 1999

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

symmetryHamiltonian systemsGauss methodsymplectic Runge-Kutta-Nyström methodsGauss-Legendre quadrature formulas

Mathematics Subject Classification ID

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) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (4)

Implicit symmetric and symplectic exponentially fitted modified Runge-Kutta-Nyström methods for solving oscillatory problems ⋮ Symmetric and symplectic exponentially fitted Runge-Kutta-Nyström methods for Hamiltonian problems ⋮ Order properties of symplectic Runge-Kutta-Nyström methods ⋮ Symmetric integrators based on continuous-stage Runge-Kutta-Nyström methods for reversible systems

Cites Work

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• Order conditions for canonical Runge-Kutta-Nyström methods
• Runge-Kutta schemes for Hamiltonian systems
• Canonical Runge-Kutta-Nyström (RKN) methods for second order ordinary differential equations
• A theory for Nyström methods
• Méthodes de Nystrom pour l'équation différentielle y=f(x,y)
• Reducibility and characterization of symplectic Runge-Kutta methods
• An Explicit Runge–Kutta–Nyström Method is Canonical If and Only If Its Adjoint is Explicit
• Implicit Runge-Kutta Processes

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