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Computational uncertainty and the application of a high-performance multiple precision scheme to obtaining the correct reference solution of Lorenz equations

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Abstract

The computational uncertainty principle (CUP) is applied to explain the experimental formulae of the critical time of decoupling for Lorenz equations (LEs). We apply the multiple precision (MP) library in obtaining the long-time solution of LEs, and based on the classic Taylor scheme, we developed a high-performance parallel Taylor solver to do the computation. The new solver is several hundreds times faster than the reported solvers developed in MATHEMATICA software, and it has the ability to yield longer solutions of LEs, up to t ∼ 104 LTU (Lorenz time unit). Further, we notice that the two computation processes with different precisions or orders will produce the reliable correct reference solutions before they have a significant difference. According to this property we propose an approach for maintaining the correct numerical solution. The new solver and the solution validation approach are used to identify and correct an erroneous solution reported in a previous study.

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Authors and Affiliations

  1. State Key Laboratory of Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

    Pengfei Wang & Jianping Li

  2. Graduate University of Chinese Academy of Sciences, Beijing, China

    Pengfei Wang

  3. Key Laboratory of Middle Atmosphere and Global Environment Observation (LAGEO), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

    Qian Li

Authors
  1. Pengfei Wang
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  2. Jianping Li
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  3. Qian Li
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Correspondence to Pengfei Wang.

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Wang, P., Li, J. & Li, Q. Computational uncertainty and the application of a high-performance multiple precision scheme to obtaining the correct reference solution of Lorenz equations. Numer Algor 59, 147–159 (2012). https://doi.org/10.1007/s11075-011-9481-6

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  • DOI: https://doi.org/10.1007/s11075-011-9481-6

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