Clean numerical simulation for some chaotic systems using the parallel multiple-precision Taylor scheme  

作　　者：Pengfei Wang Yong Liu Jianping Li 

机构地区：[1]Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences [2]State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences

出　　处：《Chinese Science Bulletin》2014年第33期4465-4472,共8页

基　　金：supported by the National Basic Research Program of China(2011CB309704);the National Natural Science Foundation of China(41375112)

摘　　要：An improved parallel multiple-precision Taylor(PMT) scheme is developed to obtain clean numerical simulation(CNS) solutions of chaotic ordinary differential equations(ODEs). The new version program is about 500 times faster than the reported solvers developed in the MATHEMATICA, and also 2–3 times faster than the older version(PMT-1.0) of the scheme. This solver has the ability to yield longer solutions of Lorenz equations [up to5000 TU(time unit)]. The PMT-1.1 scheme is applied to a selection of chaotic systems including the Chen, Rossler,coupled Lorenz and Lu¨ systems. The Tc-M and Tc-K diagrams for these chaotic systems are presented and used to analyze the computation parameters for long-term solutions. The reliable computation times of these chaotic equations are obtained for single- and double-precision computation.An improved parallel multiple-precision Taylor （PMT） scheme is developed to obtain clean numerical simulation （CNS） solutions of chaotic ordinary differential equations （ODEs）. The new version program is about 500 times faster than the reported solvers developed in the MATHEMATICA, and also 2-3 times faster than the older version （PMT-1.0） of the scheme. This solver has the ability to yield longer solutions of Lorenz equations [up to 5000 TU （time unit）]. The PMT-1. I scheme is applied to a selection of chaotic systems including the Chen, Rossler, coupled Lorenz and Lti systems. The Tc-M and Tc-K diagrams for these chaotic systems are presented and used to analyze the computation parameters for long-term solutions. The reliable computation times of these chaotic equations are obtained for single- and double-precision computation.

关 键 词：混沌系统 精度计算 数值模拟 泰勒 并行 常微分方程 LTI系统 数学发展 

分 类 号：O241.81[理学—计算数学]