期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 201, 期 1, 页码 13-33出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2004.04.018
关键词
continuation methods; periodic orbits; Poincare maps; variational equations; Krylov methods; Arnoldi decomposition; subspace iteration
Efficient numerical algorithms for the continuation of periodic orbits of high-dimensional dissipative dynamical systems, and for analyzing their stability are presented. They are based on shooting, Newton-Krylov and Arnoldi methods. A thermal convection fluid dynamics problem, which has a rich bifurcation diagram due to symmetries, has been used as test. After a pseudo-spectral discretization of the equations a system of dimension O(10(4)) has been obtained. The efficiency of the algorithms, which allows the unfolding of a complex diagram of periodic orbits, makes the methods suitable for the study of large nonlinear dissipative partial differential equations. (C) 2004 Elsevier Inc. All rights reserved.
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