Jacobi Algorithm for solving Laplace's Equation, to observe
The important part of the algorithm is applied in the function which
sets up the two-dimensional Laplace equation. There we have a while
statement which tests the difference between the temporary vector and
the solution \( u_{i,j} \). Moreover, we have fixed the number of
iterations to a given maximum. We need also to provide a convergence
tolerance. In the above program example we have fixed this to be
\( 0.00001 \). Depending on the type of applications one may have to
change both the number of maximum iterations and the tolerance.