COMPUTATION OF INVARIANT TORI BY THE METHOD OF CHARACTERISTICS

被引:36
作者
DIECI, L [1 ]
LORENZ, J [1 ]
机构
[1] UNIV NEW MEXICO,DEPT MATH & STAT,ALBUQUERQUE,NM 87131
关键词
INVARIANT TORI; LOCAL COORDINATE SYSTEM; METHOD OF CHARACTERISTICS; COUPLED OSCILLATOR; VAN DER POL OSCILLATOR; INVARIANT CURVE; POINCARE MAP;
D O I
10.1137/0732066
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we present a technique for the numerical approximation of a branch of invariant tori of finite-dimensional ordinary differential equations systems. Our approach is a discrete version of the graph transform technique used in analytical work by Fenichel [Indiana Univ. Math. J., 21 (1971), pp. 193-226]. In contrast to our previous work [L. Dieci, J. Lorenz, and R. D. Russell, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 607-647], the method presented here does not require a priori knowledge of a suitable coordinate system for the branch of invariant tori, but determines and updates such a coordinate system during a continuation process. We give general convergence results for the method and present its algorithmic description. We also show how the method performs on two physically important nonlinear problems, a system of two coupled oscillators and the forced van der Pol oscillator. In the latter case, we discuss some modifications needed to approximate an invariant curve for the Poincare map.
引用
收藏
页码:1436 / 1474
页数:39
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