Nizare Riane

Nizare Riane, Claire David

In the sequel, we extend our previous work on the Minkowski Curve to Sierpiński 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.

Nizare Riane, Claire David

In this work, we describe how to approximate solutions of some partial differential equations using the finite difference method defined on the Minkowski self-similar curve.