A geometrical method for the Smoluchowski equation on the sphere

A study of the diffusion a passive Brownian particle on surface sphere and subject to effects an external potential, coupled linearly probability density particle's position, is presented through numerical algorithm devised simulate trajectories ensemble particles. The based elementary geometry practically only algebraic operations are used, which makes efficient simple, converges, in \textit{weak sense}, solutions Smoluchowski equation sphere. Our findings show that global curvature taken into account both time dependent stationary processes.