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A B-spline finite element method is used to solve the equal width equation numerically. This approach involves a collocation method using quintic B-splines at the knot points as element shape. Time integration of the resulting system of ordinary differential equations is effected using the fourth order Runge–Kutta method, instead of the finite difference… (More)

A numerical method based on the Adomian decomposition method which has been developed by Adomian [Adomian, MA] is introduced in this paper for the approximate solution of delay differential equation (DDE). The algorithm is illustrated by studying an initial value problem. The results obtained are presented and show that only few terms are required to obtain… (More)

The time-delayed Burgers equation is introduced and the improved tanh-function method is used to construct exact multiple soliton and triangular periodic solutions. For an understanding of the nature of the exact solutions that contained the time-delay parameter, we calculated the numerical solutions of this equation by using the Adomian decomposition… (More)

We consider solitary wave solutions of the generalized equal width (GEW) wave equation u t + εu p u x − δu xxt = 0. This paper presents a collocation method for the GEW equation, which is classified as a nonlinear PDE using quadratic B-splines at midpoints as element shape functions. In this research, the scheme of the equation under investigation is found… (More)