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Numerical Analysis of the Mixed 4th-Order Runge-Kutta Scheme of Conditional Nonlinear Optimal Perturbation Approach for the EI Niño-Southern Oscillation Model

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  19 September 2016

Xin Zhao ,
Jian Li ,
Wansuo Duan  and
Dongqian Xue
Xin Zhao*
Affiliation:
College of Tourism and Environment, Shaanxi Normal University, Shaanxi 720062, China Weihe River Basin Resources and Environment and Ecological Civilization, Institute of Computational Mathematics and Its Applications, Baoji University of Arts and Sciences, Shaanxi 721013, China
Jian Li*
Affiliation:
Weihe River Basin Resources and Environment and Ecological Civilization, Institute of Computational Mathematics and Its Applications, Baoji University of Arts and Sciences, Shaanxi 721013, China
Wansuo Duan*
Affiliation:
LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
Dongqian Xue*
Affiliation:
College of Tourism and Environment, Shaanxi Normal University, Shaanxi 720062, China
*
*Corresponding author. Email:sungirl_zhx@163.com (X. Zhao), jiaaanli@gmail.com (J. Li), duanws@lasg.iap.ac.cn (W. S. Duan), xuedq@snnu.edu.cn (D. Q. Xue)
*Corresponding author. Email:sungirl_zhx@163.com (X. Zhao), jiaaanli@gmail.com (J. Li), duanws@lasg.iap.ac.cn (W. S. Duan), xuedq@snnu.edu.cn (D. Q. Xue)
*Corresponding author. Email:sungirl_zhx@163.com (X. Zhao), jiaaanli@gmail.com (J. Li), duanws@lasg.iap.ac.cn (W. S. Duan), xuedq@snnu.edu.cn (D. Q. Xue)
*Corresponding author. Email:sungirl_zhx@163.com (X. Zhao), jiaaanli@gmail.com (J. Li), duanws@lasg.iap.ac.cn (W. S. Duan), xuedq@snnu.edu.cn (D. Q. Xue)
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Abstract

In this paper, we proposes and analyzes the mixed 4th-order Runge-Kutta scheme of conditional nonlinear perturbation (CNOP) approach for the EI Niño-Southern Oscillation (ENSO) model. This method consists of solving the ENSO model by using a mixed 4th-order Runge-Kutta method. Convergence, the local and global truncation error of this mixed 4th-order Runge-Kutta method are proved. Furthermore, optimal control problem is developed and the gradient of the cost function is determined.

Keywords

The EI Niño-Southern Oscillation (ENSO) model4th-order Runge-Kutta schemeoptimal control problemconditional nonlinear perturbation

MSC classification

Secondary: 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016 , pp. 1023 - 1035
Copyright
Copyright © Global-Science Press 2016 

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References

[1] Wang, B. and Fang, Z., Chaotic oscillation of tropical climate: A dynamic system theory for ENSO, J. Atmos. Sci., 53 (1996), pp. 2786–2802.2.0.CO;2>CrossRefGoogle Scholar
[2] Lorenz, E., A study of the predictability of a 28-variable atmospheric model, Tellus, 17 (1965), pp. 321–333.CrossRefGoogle Scholar
[3] Mu, M. and Duan, W., A new approach to studying ENSO predictability: conditional nonlinear optimal perturbation, Chinese Sci. Bull., 48 (2003), pp. 1045–1047.CrossRefGoogle Scholar
[4] Mu, M., Duan, W. and Wang, B., Conditional nonlinear optimal perturbation and its applications, Nonlin. Processes Geophys., 10 (2003), pp. 493–501.CrossRefGoogle Scholar
[5] Mu, M., Duan, W., Wang, Q. and Zhang, R., An extension of conditional nonlinear optimal perturbation approach and its applications, Nonlinear Processes Geophys., 17 (2010), pp. 211–220.Google Scholar
[6] Mu, M., Duan, W. and Wang, B., Season-dependent dynamics of nonlinear optimal error growth and El Niño Oscillation predictability in a theoretical model, J. Geophys. Res., 112 (2007), pp. 211–220.Google Scholar
[7] Mu, M., Xu, H. and Duan, W., A kind of initial errors related to “spring predictability barrier” for El Niño events in Zebiak-Cane model, Geophys. Res. Lett., 34 (2007), pp. 211–220.Google Scholar
[8] Cartwright, J. H. E. and Piro, O., The dynamics of Runge–Kutta methods, Int. J. Bifurcation Chaos, 2 (1992), pp. 427C–449.CrossRefGoogle Scholar
[9] Lions, J.-L., Optimal Control of Systems Governed by Partial Differential Equations, Springer, Berlin-Heidelberg-New York, 1971.CrossRefGoogle Scholar
[10] Fursikov, A. V., Optimal Control of Distributed Systems: Theory and Applications, Vol. 187, Trans l. Math. Monogr. AMS, Providence, 1999.CrossRefGoogle Scholar