A model for the simulation of light curves of single magnetically active spotted stars has been developed. Simulated light curves are qualitatively compared to observed ones and quantitatively analysed by means of Fourier analysis. The time variable light modulation induced by an evolving spot pattern on a differentially rotating star is studied in order to test the capability of the Fourier analysis, by the Scargle method, to extract information on differential rotation. Light curve precision of DELTAF/F = 10(-5) - 10(-6), where F is the stellar flux, and uninterrupted time coverage of at least 2pi/DELTAOMEGA, where OMEGA is the angular velocity, prove adequate to detect differential rotation of the order of DELTAOMEGA. Such a result shows the importance of dedicated long term observations by space-borne telescopes.