The Spherical Symmetric Diffusion Problem

Evgenii B. Krissinel' and Noam Agmon

We introduce a general and versatile MS Windows application for solving the spherically symmetric diffusion problem, involving up to two coupled spherically symmetric Smoluchowski equations. It is based on a modular, configurable, user-friendly graphical interface, in which input parameters are introduced through a graphical representation of the system of partial differential equations and output attributes can be obtained graphically during propagation. The numerical algorithm consists of finite differencing in space and Chebyshev propagation in time. It includes an implementation of virtual-gridding, which enhances the accuracy of calculating boundary conditions and steep potentials. The program has been checked against a wide collection of analytical solutions and applied to an experimentally open problem in excited-state proton-transfer to solvent.