In this article, a mathematical model representing solution of the nonlinear generalized equal width (GEW) equation has been considered. Here we aim to investigate solutions of GEW equation using a numerical scheme by using sextic B-spline Subdomain finite element method. At first Galerkin finite element method is proposed and a priori bound has been established. Then a semi-discrete and a Crank-Nicolson Galerkin finite element approximation have been studied respectively. In addition to that a powerful Fourier series analysis has been performed and indicated that our method is unconditionally stable. Finally, proficiency and practicality of the method have been demonstrated by illustrating it on two important problems of the GEW equation including propagation of single solitons and collision of double solitary waves. The performance of the numerical algorithm has been demonstrated for the motion of single soliton by computing $L_{\infty }$ and $L_2$ norms and for the other problem computing three invariant quantities $I_1,I_2$ and $I_3$. The presented numerical algorithm has been compared with other established schemes and it is observed that the presented scheme is shown to be effectual and valid.

在本文中，已经考虑了代表非线性广义等宽（GEW）方程解的数学模型。在这里，我们的目的是通过使用正弦B样条子域有限元方法，采用数值方案研究GEW方程的解。首先提出了Galerkin有限元方法，并建立了先验界。然后分别研究了半离散和Crank-Nicolson Galerkin有限元逼近。此外，已经进行了功能强大的傅里叶级数分析，并表明我们的方法是无条件稳定的。最后，通过说明GEW方程的两个重要问题，包括单孤子的传播和双孤波的碰撞，证明了该方法的实用性和实用性。${\mathrm{大号}}_{\infty }$ 和 ${\mathrm{大号}}_2$ 范数和其他问题，计算三个不变量 ${\mathrm{一世}}_{\mathrm{1个}}，{\mathrm{一世}}_2$ 和 ${\mathrm{一世}}_3$。所提出的数值算法已经与其他已建立的方案进行了比较，并且观察到所提出的方案被证明是有效和有效的。