DISCRETE OPERATOR INFLUENCE ON THE PROPERTIES OF NONLINEAR DYNAMICAL SYSTEMS

In this paper, we study the influence of a discrete operator (a numerical integration method) on the time behavior and qualitative properties of nonlinear dynamical systems. Methods of numerical integration of three classes are considered: explicit, implicit and semi-implicit. A methodology for determining the volume of the phase space of nonlinear dynamical systems is presented. A methodology for constructing the implicit midpoint method and the semi-implicit Wehrle method for an arbitrary system of ordinary differential equations is presented. Experimental studies are carried out on two systems: a model of a nonlinear harmonic oscillator and a model that implements the gravitational problem of N bodies. For each model, the results of long-term modeling and estimation of the phase volume of the system using explicit, implicit and semi-implicit methods are presented. The advantages and disadvantages of using each class of numerical integration methods in modeling the considered mathematical systems are presented. Conclusions are drawn about the applicability of the considered methods in modeling nonlinear Hamiltonian systems.

Authors: S. V. Goryainov, Sh. S. Fahmi, S. A. Panov

Direction: Informatics, Computer Technologies And Control

Keywords: Numerical integration methods, phase space volume, N-body problem, discrete operator, harmonic oscillator, Verlet method, implicit midpoint method

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