The current paper concerns to develop an efficient and robust numerical technique to solve the shallow water equation based on the generalized equal width (GEW) model. The considered model i.e. the generalized equal width (GEW) equation is a PDE that it can be classified in the category of hyperbolic PDEs. The solution of hyperbolic PDEs is similar to a fixed or moving wave. Thus, for solving these problems, a suitable numerical procedure that its basis functions are similar to a flat or shape wave should be selected. For this aim, the local collocation method via two different basis functions is utilized. First, the space derivative is approximated by the local collocation procedure that this manner yields a system of nonlinear ODEs depends on the time variable. Furthermore, the constructed system of ODEs is solved by a fourth-order algorithm to get high-numerical results. The mentioned process is applied on several test problems to verify the efficiency of the numerical formulation.

当前的论文涉及开发一种有效且稳健的数值技术来求解基于广义等宽 (GEW) 模型的浅水方程。所考虑的模型，即广义等宽 (GEW) 方程是一个偏微分方程，它可以归类为双曲偏微分方程。双曲偏微分方程的解类似于固定波或移动波。因此，为了解决这些问题，应该选择一个合适的数值程序，其基函数类似于平面或形状波。为此，利用了通过两个不同基函数的局部搭配方法。首先，空间导数由局部搭配程序近似，这种方式产生一个非线性 ODE 系统，取决于时间变量。此外，构造的 ODE 系统通过四阶算法求解以获得高数值结果。上述过程应用于几个测试问题，以验证数值公式的有效性。