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Abstract
In previous decades, many of the practical problems arising in scientific fields such as mathematics, physics, chemistry, biology,and engineering have been related to nonlinear fractional partial differential equations. One of these nonlinear partial differential equations, the third-order dispersive partial differential equation, has been found to have a plethora of useful applications in different fields such as Newtonian fluid mechanics, optimal control, convection diffusion processes, hydrodynamics, and aerodynamics. A special class of solutions has been studied for the third-order dispersive partial differential equation including exact solutions and approximate solutions. The aim of this article is to compare were the Adomian decomposition method, the lines method, an exponential quartic spline and finite difference discretization method, and the non-polynomial spline methodwith the solution of the third-order dispersive partial differential equation. We will conduct a comparison of the stability of the two methods using the Von Neumann stability analysis. In addition, a numerical example will be presented to illustrate the accuracy of these methods.
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