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.
基金
supported by the National Basic Research Program of China(2011CB309704)
the National Natural Science Foundation of China(41375112)
