Open Access

ARTICLE

Numerical Validations of the Tangent Linear Model for the Lorenz Equations

Tengjin Zhao¹, Jing Zhang¹, Zhilin Li², Zhiyue Zhang^1,*

1 School of Mathematical Sciences, Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing, 210023, China.
2 Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA.

*Corresponding Author: Zhiyue Zhang. Email: .

Computer Modeling in Engineering & Sciences 2019, 120(1), 83-104. https://doi.org/10.32604/cmes.2019.04483

Abstract

The validity of the tangent linear model (TLM) is studied numerically using the example of the Lorenz equations in this paper. The relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method. A new error function between the nonlinear and the linear evolution of the perturbations is proposed. Furthermore, numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM, such as the initial perturbation, the prediction time, the time step size and so on, by the method of mathematical statistics.

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Keywords

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