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论文类型：期刊论文

发表时间：2010-01-01

发表刊物：DISCRETE DYNAMICS IN NATURE AND SOCIETY

收录刊物：SCIE、Scopus

卷号：2010

ISSN号：1026-0226

摘要：This paper presents two methods for accurately computing the periodic regions' centers. One method fits for the general M-sets with integer index number, the other fits for the general M-sets with negative integer index number. Both methods improve the precision of computation by transforming the polynomial equations which determine the periodic regions' centers. We primarily discuss the general M-sets with negative integer index, and analyze the relationship between the number of periodic regions' centers on the principal symmetric axis and in the principal symmetric interior. We can get the centers' coordinates with at least 48 significant digits after the decimal point in both real and imaginary parts by applying the Newton's method to the transformed polynomial equation which determine the periodic regions' centers. In this paper, we list some centers' coordinates of general M-sets' k-periodic regions (k = 3, 4, 5, 6) for the index numbers alpha = -25, -24, ..., -1, all of which have highly numerical accuracy.