The Finite Difference Method, for the heat equation on Sierpi\'{n}ski simplices

In the sequel, we extend our previous work on the Minkowski Curve to Sierpi'{n}ski simplices (Gasket and Tetrahedron), in the case of the heat equation. First, we build the finite difference scheme. Then, we give a theoretical study of the error, compute the scheme error, give stability conditions, and prove the convergence of the scheme. Contrary to existing work, we do not call for approximations of the eigenvalues.