Invariants and numerical methods for ODEs

DOI10.1016/0167-2789(92)90246-JzbMath0779.34012MaRDI QIDQ687819

C. William Gear

Publication date: 28 November 1993

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

numerical integrationdifferential invariantssymplectic invariantspoint invariantspreservation of some invariants

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for ordinary differential equations (65L99) Numerical analysis in abstract spaces (65J99)

Related Items

The generalized fractional Benjamin-Bona-Mahony equation: analytical and numerical results, Computing for pattern forming systems in nonlinear optics, On the nonlinear stability of the 1:1:1 ABC flow, Block predictor-corrector schemes for the parallel solution of ODEs, Energy--work connection integration schemes for mechanico-electrical systems, Error propagation when approximating multi-solitons: The KdV equation as a case study, Multiple-relaxation Runge Kutta methods for conservative dynamical systems, Does variable step size ruin a symplectic integrator?, Time behaviour of the error when simulating finite-band periodic waves. The case of the KdV equation, Error propagation in the numerical integration of solitary waves. The regularized long wave equation, A high-order energy-conserving integration scheme for Hamiltonian systems, Error propagation in numerical approximations near relative equilibria

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Runge-Kutta schemes for Hamiltonian systems
• Towards explicit methods for differential algebraic equations
• Symplectic integration of Hamiltonian systems
• Some properties of methods for the numerical integration of systems of the form
• Order Conditions for Canonical Runge–Kutta Schemes
• Explicit Canonical Methods for Hamiltonian Systems
• Stability Criteria for Implicit Runge–Kutta Methods
• Maintaining Solution Invariants in the Numerical Solution of ODE<scp>s</scp>
• Stability of Computational Methods for Constrained Dynamics Systems
• Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods