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

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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