Title :
Computer simulation of chaotic systems with symmetric extrapolation methods
Author :
Butusov, D.N. ; Karimov, A.I. ; Andreev, V.S.
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.
Keywords :
chaos; differential equations; extrapolation; integration; nonlinear dynamical systems; parallel algorithms; Aitken-Neville extrapolation scheme; Sprott chaotic nonlinear system; chaotic behavior; computer simulation; global truncation error analysis; nonlinear dynamical systems; numerical simulation; parallel computers; single-step semiimplicit method; symmetric ODE solver; symmetric extrapolation methods; symmetric numerical integration method; Accuracy; Chaos; Computational modeling; Computer simulation; Extrapolation; Finite wordlength effects; Numerical models; computer simulation; deterministic chaos; dynamical systems; extrapolation methods; numerical integration; symmetric methods;
Conference_Titel :
Soft Computing and Measurements (SCM), 2015 XVIII International Conference on
Conference_Location :
St. Petersburg
Print_ISBN :
978-1-4673-6960-2
DOI :
10.1109/SCM.2015.7190416
