NUMERICAL SOLUTION OF A PARABOLIC EDP ABOUT AN ISOSCELES TRIANGLE USING THE FINITE DIFFERENCE METHOD

Abstract

In this work we present the numerical resolution of an initial and boundary value problem associated to one non-homogeneous
parabolic EDP over a 2D domain with an isosceles triangle shape, using the explicit finite difference method (FDM) on an uniform mesh. The proposed numerical scheme combines a nine points stencil to approximate the solution in the nodes not
adjacent to the boundary represented by the hypotenuse, and another one of eight points to approximate the solution in those
that are adjacent to such boundary. By a standard analysis of FDM's it is demonstrated that the numerical scheme is stable, and
this result is corroborated with numerical experiments.