Computer simulation of chaotic systems with symmetric extrapolation methods

Abstract

Numerical simulation of nonlinear dynamical systems with the chaotic behavior is the major research field in a modern computer science. The aim of this research was the experimental study of new symmetric numerical integration method as a basic method for the Aitken-Neville extrapolation scheme. The properties of the Sprott (B) chaotic nonlinear system was studied via computer simulation, and the global truncation error was analyzed for the extrapolation methods of accuracy order 4 and 6. Some conclusions about the advantages of proposed symmetric ODE solver compared to the classical Runge-Kutta and Gregg-Bulirsch-Stoer methods are given. The considered extrapolation scheme has a single-step semi-implicit method as a basic solver, and is more numerically effective while being implemented on parallel computers.