COMPARATIVE STUDY OF THE LAPLACE-ADOMIAN METHOD AND THE VARIATIONAL ITERATIONS METHOD FOR DETERMINING THE EXACT SOLUTIONS OF SOME PARTIAL DIFFERENTIAL EQUATIONS

This work is a verification of the effectiveness of Laplace-Adomian and variational iterations methods for solving partial differential equations. The coupling of Laplace and Adomian methods has made it possible to exploit Adomian polynomials with Laplace transforms, as well as their inverse, to overcome the difficulties associated with the non-linearity of the equations. The variational iteration method, with its correction functional, facilitates the determination of the general Lagrange multiplier, which is essential for the rest of the solution. These methods have enabled us to obtain the exact solutions.