A Solution to the non Linear Korteweg-De-Vries Equation in the Particular Case Dispersion-Adsorption Problem in Porous Media Using the Spectral Boubaker Polynomials Expansion Scheme (BPES)

Abstract

In this study, a polynomial expansion method is proposed for solving the Korteweg-de-Vries (KdV) equation with Dirichlet-type initial-boundary values. The problem concerns simultaneous dispersion and adsorption of a solute within finite porous media with flow and dispersion in opposite directions, which corresponds i. e. to the possible control of spreading of poor-quality fluid by oppositely applied freshwater flow. The obtained results are compared with exact solutions in order to evaluate protocol exactness.