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Mathematical Problems in Engineering
Volume 2015, Article ID 573894, 15 pages
Research Article

A Class of Parameter Estimation Methods for Nonlinear Muskingum Model Using Hybrid Invasive Weed Optimization Algorithm

1College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan 410082, China
2School of Information Science and Engineering, Hunan City University, Yiyang, Hunan 413000, China
3Department of Mathematics and Computer Science, Chizhou College, Chizhou, Anhui 247000, China
4College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China

Received 27 January 2015; Revised 7 May 2015; Accepted 18 May 2015

Academic Editor: Gisele Mophou

Copyright © 2015 Aijia Ouyang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonlinear Muskingum models are important tools in hydrological forecasting. In this paper, we have come up with a class of new discretization schemes including a parameter to approximate the nonlinear Muskingum model based on general trapezoid formulas. The accuracy of these schemes is second order, if , but interestingly when , the accuracy of the presented scheme gets improved to third order. Then, the present schemes are transformed into an unconstrained optimization problem which can be solved by a hybrid invasive weed optimization (HIWO) algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the present methods. The numerical results substantiate the fact that the presented methods have better precision in estimating the parameters of nonlinear Muskingum models.