Algebraic calculation of stroboscopic maps of ordinary, nonlinear differential equations
- Max-Planck-Institut fuer Extraterrestrische Physik, Garching (Germany)
- Illinois Univ., Urbana, IL (United States). Center for Complex Systems Research
- Los Alamos National Lab., NM (United States) California Univ., Santa Cruz, CA (United States). Dept. of Mathematics
The relation between the parameters of a differential equation and corresponding discrete maps are becoming increasingly important in the study of nonlinear dynamical systems. Maps are well adopted for numerical computation and several universal properties of them are known. Therefore some perturbation methods have been proposed to deduce them for physical systems, which can be modeled by an ordinary differential equation (ODE) with a small nonlinearity. A new iterative, rigorous algebraic method for the calculation of the coefficients of a Taylor expansion of a stroboscopic map from ODE's with not necessarily small nonlinearities is presented. It is shown analytically that most of the coefficients are small for a small integration time and grow slowly in the course of time if the flow vector field of the ODE is polynomial and if the ODE has fixed point in the origin. Approximations of different orders respectively of the rest term are investigated for several nonlinear systems. 31 refs., 16 figs.
- Research Organization:
- Lawrence Livermore National Lab., CA (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 5306003
- Report Number(s):
- LA-UR-91-2965; CONF-9105242-2; ON: DE92000220
- Resource Relation:
- Conference: Experimental mathematics: computational issues in nonlinear science, Los Alamos, NM (United States), 20-24 May 1991
- Country of Publication:
- United States
- Language:
- English
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