The elliptic partial differential equation, i.e. Eq. 1,
is defined in subroutine pde(x,y,p,q,r,f). The point
is passed in through the real variables x and
y. The user defines the functions 
, 
,
, and 
from Eq. 1 and returns them
through the real variables p, q, r and f. Notice
that the form of the differential operator in Eq. 1
has a minus sign in front of the second order terms. You should
be very careful to get the signs correct in the expressions
for p, q, r and f.