In the most general form the integral equations we have to solve is written as
![]() |
(10.21) |
Now we do discretization with spacing . The equation (A.22) now
can be expressed in the matrix form:
![]() |
(10.23) |
![]() |
(10.24) |
For a uniform grid very good precision is achieved using the Simpson method. The
matrix in this case is defined as
. The residual term of the integration is very
small and can be estimated as
and the error in the energy (which is defined by integrating the solution
with the weight proportional to
) is proportional to the spacing
to
the forth power.