On the properties of numerical solutions of dynamical systems obtained using the midpoint method
Journal: Discrete and Continuous Models and Applied Computational Science (Vol.27, No. 3)Publication Date: 2020-01-22
Authors : Vladimir Gerdt; Mikhail Malykh; Leonid Sevastianov; Yu Ying;
Page : 242-262
Keywords : conservative finite-difference schemes; dynamical systems; Sage; Maple; Sage; Maple;
Abstract
The article considers the midpoint scheme as a finite-difference scheme for a dynamical system of the form ̇ = (). This scheme is remarkable because according to Cooper’s theorem, it preserves all quadratic integrals of motion, moreover, it is the simplest scheme among symplectic Runge-Kutta schemes possessing this property. The properties of approximate solutions were studied in the framework of numerical experiments with linear and nonlinear oscillators, as well as with a system of several coupled oscillators. It is shown that in addition to the conservation of all integrals of motion, approximate solutions inherit the periodicity of motion. At the same time, attention is paid to the discussion of introducing the concept of periodicity of an approximate solution found by the difference scheme. In the case of a nonlinear oscillator, each step requires solving a system of nonlinear algebraic equations. The issues of organizing computations using such schemes are discussed. Comparison with other schemes, including those symmetric with respect to permutation of and .̂
Other Latest Articles
- Geodesic motion near self-gravitating scalar field configurations
- Charge diffusion in homogeneous molecular chains based on the analysis of generalized frequency spectra in the framework of the Holstein model
- Simulation of a gas-condensate mixture passing through a porous medium in depletion mode
- Numerical analysis of ecology-economic model for forest fire fighting in Baikal region
- Characteristics of optical filters built on the basis of periodic relief reflective structures
Last modified: 2020-08-31 19:27:52