The finite difference representation of (1) is:
or, equivalently,
If we define the vector 
to be 
to
designate the 
unknown grid values, and pull out all the known
information from (30), we can reformulate (1) by its
finite difference approximation in the form of the matrix equation,
, where 
is a vector which contains the
sources and modifications due to the Dirichlet boundary condition.
