非线性系统的任意项精细积分外插多步法及其在混沌数值分析中的应用

对非线性系统提出了高精度的精细积分任意项外插多步法的计算公式.本方法只需增加插值 项数即可提高计算精度，同时不会增加过大的计算量，发展完善了精细积分法.将本方法应 用于混沌方程中，取得了较好的效果.数值计算结果表明，该方法是一种高精度、高效率的 方法，在求解混沌系统上比传统方法有很大的优势. 关键词： 非线性系统 任意项精细积分多步法 混沌系统

The free-item extrapolated multistep method for precise integration of a nonline ar system and its application in the digital analysis of a chaotic system

The free-item extrapolated multistep method for precise integration is proposedfor a nonlinear system, and the calculation formula for the free-item extrapolated multistep method is obtained. The accuracy of the extrapolated multistep me thod can be improved through increasing the number of extrapolated points; at th e same time, evaluations cannot be increased too much. The precise integration m ethod has been developed and perfected by the present studies. When the method i s applied to a chaotic system, the result is admirable. Numerical calculations s how that the present method is high by accurate and computationally efficient.It has more advantages than the traditional methods in the analysis of a chaotic s ystem.