Runge-Kutta methods for quadratic ordinary differential equations

DOI10.1007/BF02512370zbMath0908.65063OpenAlexW2080544145MaRDI QIDQ1267024

Arieh Iserles, Geetha Ramaswami, Mark Sofroniou

Publication date: 4 March 1999

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02512370

zbMATH Keywords

convergenceerror boundsRunge-Kutta-Nyström methodsorder conditionsbinary treesquadratic differential equations

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

Quadratic Störmer-type methods for the solution of the Boussinesq equation by the method of lines ⋮ Dirichlet series for dynamical systems of first-order ordinary differential equations ⋮ Unnamed Item ⋮ Semi-analytical and numerical solutions of multi-degree-of-freedom nonlinear oscillation systems with linear coupling

Uses Software

• RODAS

Cites Work

• Rigorous error analysis of numerical algorithms via symbolic computations
• Order conditions for canonical Runge-Kutta-Nyström methods
• Theory of nonlinear lattices
• A theory for Nyström methods
• Symbolic derivation of Runge-Kutta methods
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• Order stars and linear stability theory
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• Solving Ordinary Differential Equations I
• Symplectic integration of Hamiltonian systems
• Explicit Canonical Methods for Hamiltonian Systems
• One-step methods of hermite type for numerical integration of stiff systems
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