  This paper deals with the numerical methods for the reconstruction of source
term in linear parabolic equation from final overdetermination. We assume that
the source term has the form f(x)h(t) and h(t) is given, which guarantees the
uniqueness of the inverse problem for determining the source term $f(x)$ from
final overdetermination. We present the numerical methods for both free
boundary and Neumann boundary situations. Moreover, we show that the solution
of the boundary conditions problem has the form of the free boundary solution
problem by using the extension method. Numerical experiments are done for the
inverse problem with the boundary conditions.
