  Extended source effects can be seen in gravitational lensing events when
sources cross critical lines. Those events probe the stellar intensity profile
and could be used to measure limb darkening coefficients to test stellar model
predictions. A data base of accurately measured stellar profiles will be needed
to correctly subtract the stellar flux in planetary transient events. The
amount of data that is being and will be produced in current and future
microlensing surveys, from the space and the ground, requires algorithms that
can quickly compute light curves for different source-lens configurations.
Based on the convolution method we describe a general formalism to compute
those curves for single lenses. We develop approximations in terms of
quadratures of elliptic integrals that we integrate by solving the associated
first order differential equations. We construct analytic solutions for a limb
darkening and, for the first time, for a parabolic profile that are accurate at
the $\sim 1-3\%$ and $0.5\%$ level, respectively. These solutions can be
computed orders of magnitude faster than other integration routines. They can
be implemented in pipelines processing large data sets to extract stellar
parameters in real time.
