On the Existence, Uniqueness and Application of the Finite Difference Method for Solving Cauchy-Dirichlet Problem

Abstract

In this paper we treat the existence, the uniqueness and the numerical resolution of the problem at the elliptic limits case of the Cauchy-Dirichlet problem of the type the stationary convection-diffusion equation. By applying the Lax-Milgram theorem, we proved the existence and the uniqueness of the problem, then we solved the problem numerically by the finite difference method. In addition, we solved the problem analytically using the method of variation of constants. Finally, we performed a numerical simulation of said problem to approach the exact solution by the numerical solution using the software Scilab