On the exact discretization of the classical harmonic oscillator equation

DOI10.1080/10236191003730563zbMath1232.65175arXiv0911.3672OpenAlexW2964266188MaRDI QIDQ3103821

Jan L. Cieśliński

Publication date: 12 December 2011

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.3672

zbMATH Keywords

finite difference methodnumerical examplesenergy integralgeometric numerical integrationharmonic oscillator equationexact discretizations

Mathematics Subject Classification ID

Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Finite difference and finite volume methods for ordinary differential equations (65L12) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (13)

Locally exact modifications of numerical schemes ⋮ A non‐standard finite difference scheme for an advection‐diffusion‐reaction equation ⋮ An improved Störmer-Verlet method based on exact discretization for nonlinear oscillators ⋮ A new high precision energy-preserving integrator for system of oscillatory second-order differential equations ⋮ Exact discretization of Schrödinger equation ⋮ Exact discretization by Fourier transforms ⋮ Discrete gradient algorithms of high order for one-dimensional systems ⋮ New definitions of exponential, hyperbolic and trigonometric functions on time scales ⋮ Fast exact digital differential analyzer for circle generation ⋮ Improving the accuracy of the AVF method ⋮ A discrete nonlinear Schrödinger-type hierarchy, its finite-dimensional reduction analysis, and the numerical integration scheme ⋮ Locally exact modifications of discrete gradient schemes ⋮ Discrete approximations on functional classes for the integrable nonlinear Schrödinger dynamical system: a symplectic finite-dimensional reduction approach

Cites Work

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• An orbit-preserving discretization of the classical Kepler problem
• Analysis on measure chains - a unified approach to continuous and discrete calculus
• Discrete mechanics - a general treatment
• Practical symplectic methods with time transformation for the few-body problem
• A Gautschi-type method for oscillatory second-order differential equations
• A new conservative numerical integration algorithm for the three-dimensional Kepler motion based on the Kustaanheimo-Stiefel regularization theory
• Numerical integration of ordinary differential equations based on trigonometric polynomials
• Numerical integration of products of Fourier and ordinary polynomials
• Stabilization of Cowell's method
• Contributions to the mathematics of the nonstandard finite difference method and applications
• Conservative discretizations of the Kepler motion
• Comment on ‘Conservative discretizations of the Kepler motion’
• Long-time behaviour of discretizations of the simple pendulum equation
• Geometric integration using discrete gradients
• Numerical methods for Hamiltonian PDEs
• Geometric Numerical Integration
• Perturbation theory of Kepler motion based on spinor regularization.
• Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
• Stabilization of finite difference methods of numerical integration
• An algebraic, energy conserving formulation of classical molecular and Newtonian 𝑛-body interaction
• An exponential method of numerical integration of ordinary differential equations
• Differential and Difference Equations

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