An approximate solution of a separable Smoluchowski equation in one spatial dimension is constructed here in the form of a finite eigenfunction expansion. The spectrum of the Smoluchowski operator, and the corresponding eigenfunctions, are computed using the so called shooting method of adjoints. Explicit numerical solutions are presented for static and fluctuating potentials, and it is shown that for any smooth initial probablity distribution the finite expansion holds on all time scales. The method is applicable to any linear eigenproblem on a finite one-dimensional interval; the solution of the Sturm-Liouville problem has a particularly convenient form.

• Received 2 August 1999

DOI:https://doi.org/10.1103/PhysRevE.62.4469