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

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  • Computational Physics
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Chinese Science Bulletin

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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Acknowledgement

The authors thank Prof. Shijun Liao for suggestions made during helpful discussions, especially in terms of improving the computation of the Taylor coefficients. This work was jointly supported by the National Basic Research Program of China (2011CB309704) and the National Natural Science Foundation of China (41375112).

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Authors and Affiliations

  1. Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Pengfei Wang & Yong Liu

  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

    Pengfei Wang & Jianping Li

Authors
  1. Pengfei Wang
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  2. Yong Liu
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  3. Jianping Li
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Correspondence to Pengfei Wang.

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Wang, P., Liu, Y. & Li, J. Clean numerical simulation for some chaotic systems using the parallel multiple-precision Taylor scheme. Chin. Sci. Bull. 59, 4465–4472 (2014). https://doi.org/10.1007/s11434-014-0412-5

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  • DOI: https://doi.org/10.1007/s11434-014-0412-5

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