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The switching time of a single-domain particle with uniaxial anisotropy subjected to an applied field along the easy axis is studied by solving Brown's Fokker-Planck equation numerically. The equation is modified in order to be integrated by a finite-difference method. The validity of this method is verified by comparing the frequency prefactors in the exponential decay calculated by this method with the values from Brown's formula for the prefactor. Switching times for several values of the applied field and the temperature are calculated. Curves of the inverse of the switching time are fitted to a simple expression by using a least-squares method. The expression consists of two terms: a linear function of the applied field and a function proportional to the square root of the temperature. The dependence of the switching time on the magnetization, the volume of the particle, the anisotropy field, the Gilbert's damping constant, and the gyromagnetic constant is also presented.