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 θto approximate the nonlinear Muskingum model based on general trapezoid formulas. The accuracy of these schemes is second order, if θ≠1/3, but interestingly when θ= 1/3, 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...
