The Classical Smoluchowski Equation

During the last years with the studies of stochastic processes: neurons networks, molecular motors, dynamics models, anomalous diffusion, disordered media, etc, several methods have evolved to apply the Focker-Planck equation (FPE) to these phenomena. We present here the solution of the Fokker-Planck equation by the Crank-Nicholson formalism. The von Neumann amplification factor, \(\xi \left ( k\right ) \) , is independent of dt, so the method is stable for any size dt. The method is suitable for modeling molecular motors because the great amount of interactions in these systems, vectors and matrixs oriented methods are needed, suited to work with Matlab.