Abstract
The main objective of the following document is to present an approximate numerical solution of the Korteweg de Vries (KdV) equation, since it has a wide field of applications, such as acoustics, molecular biology, optics, and quantum mechanics. For this, the basic concepts associated with the numerical method that will be used to obtain the approximate solution will be presented initially, in our case, the finite element method and in particular the Galerkin method. A further understanding of the effectiveness of the method is achieved by presenting an analytical solution considering the wave speed as a constant and performing a change of variable. Subsequently, the approximate numerical solution for different times is compared with the analytical solution obtained. As a secondary objective, we propose different simulations corresponding to the analytical solution for different times, the approximate solution through the Galerkin method to observe the behavior of the displacement of a particle on the wave in one dimension. Keywords: Approximate Solution, Finite Element Method, The Galerkin Solution, KdV Equation, Nonlinear Equation DOI： https://doi.org/10.35741/issn.0258-2724.58.3.34
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