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Extended source effects can be seen in gravitational lensing events whensources cross critical lines. Those events probe the stellar intensity profileand could be used to measure limb darkening coefficients to test stellar modelpredictions. A data base of accurately measured stellar profiles will be neededto correctly subtract the stellar flux in planetary transient events. Theamount of data that is being and will be produced in current and futuremicrolensing surveys, from the space and the ground, requires algorithms thatcan quickly compute light curves for different source-lens configurations.Based on the convolution method we describe a general formalism to computethose curves for single lenses. We develop approximations in terms ofquadratures of elliptic integrals that we integrate by solving the associatedfirst order differential equations. We construct analytic solutions for a limbdarkening and, for the first time, for a parabolic profile that are accurate atthe $\sim 1-3\%$ and $0.5\%$ level, respectively. These solutions can becomputed orders of magnitude faster than other integration routines. They canbe implemented in pipelines processing large data sets to extract stellarparameters in real time.

Fast Computational Convolution Methods For Extended Source Effects In Microlensing Lightcurves