In this paper, a fully implicit finite difference method is presented to solve the generalized equal width equation. This implicit method allows to handle any values of p. Since the equation is nonlinear the scheme leads to a system of nonlinear equations. At each time step, Newton’s method is used to solve this nonlinear system. The linear stability analysis of the proposed method is investigated using von Neumann approach and at the end of this investigation is seen that the method is unconditionally stable. The results are comparisons with analytical and other numerical values clearly show that results obtained using the fully implicit finite difference scheme are precise and reliable.

中文翻译：

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广义等宽（GEW）方程数值解的完全隐式有限差分方法

本文提出了一种完全隐式的有限差分方法来求解广义等宽方程。这种隐式方法允许处理p的任何值。由于方程是非线性的，因此该方案导致了一个非线性方程组。在每个时间步，牛顿方法都用于求解该非线性系统。使用冯·诺伊曼方法研究了该方法的线性稳定性分析，并在研究结束时看到该方法是无条件稳定的。将结果与分析值和其他数值进行比较，清楚地表明，使用完全隐式有限差分方案获得的结果准确而可靠。