Clean numerical simulation for some chaotic systems using the parallel multiple-precision Taylor scheme |
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| Authors: | Pengfei Wang Yong Liu Jianping Li |
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| Institution: | 1. Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100190, China
2. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China
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| Abstract: | 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-1.1 scheme is applied to a selection of chaotic systems including the Chen, Rossler, coupled Lorenz and Lü systems. The T c -M and T c -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. |
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| Keywords: | Taylor scheme Parallel multiple- precision computation Chaotic dynamic systems |
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