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  

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

作　　者：唐晨[1] 张皞[1] 闫海青[1] 张桂敏[1] 

机构地区：[1]天津大学应用物理系

出　　处：《物理学报》2003年第5期1091-1095,共5页Acta Physica Sinica

基　　金：上海交通大学振动;冲击;噪声国家重点实验 (批准号 :VSN 2 0 0 3 0 3);天津大学"985教育振兴计划"资助的课题~~

摘　　要：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 。The free-item extrapolated multistep method for precise integration is proposed for a nonlinear system, and the calculation formula for the free - item extrapolated multistep method is obtained. The accuracy of the extrapolated multistep method can be improved through increasing the number of extrapolated points; at the same time, evaluations cannot be increased too much. The precise integration method has been developed and perfected by the present studies. When the method is applied to a chaotic system, the result is admirable. Numerical calculations show 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 system.

关 键 词：非线性系统 任意项精细积分外插多步法 混沌系统 混沌吸引子 混沌方程 数值计算 

分 类 号：O415.5[理学—理论物理]