Jacobi Algorithm for solving Laplace's Equation
It is thus fairly straightforward to extend this equation to the
three-dimensional case. Whether we solve Eq.
(17)
or Eq.
(18), the solution strategy remains the same.
We know the values of
u at
i=0 or
i=n+1 and at
j=0 or
j=n+1 but we cannot start at one of the boundaries and work our way into and
across the system since Eq.
(17) requires the knowledge
of
u at all of the neighbouring points in order to calculate
u at any
given point.