Elliptic PDE's

It is often the case that the boundary values for the functionu(x,y)are known at all points on the sides of a rectangular regionRin the plane. In this case, each of these equations can be solved by the numerical technique known as the finite-difference method.

Program Dirichlet Method for Laplace's equation)

To approximate the solution of the Laplace's equation

over the rectangle

with

,

,for

,and

,for

.It is assumed that

and integersnandmexist so that

.