Article contents
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
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.
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MSC classification
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- Research Article
- Information
- Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016 , pp. 1023 - 1035
- Copyright
- Copyright © Global-Science Press 2016
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
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