A New Algorithm for the Numerical Solution of Diffusion Problems Related to the Smoluchowski Equation

Abstract

Diffusion-influenced reactions can often be described with simple kinetic models, whose basic features are a spherically symmetric potential, a distance-dependent relative diffusion coefficient, and a distance-dependent first-order rate coefficient. A new algorithm for the solution of the corresponding Smoluchowski equation has been developed. Its peculiarities are: (1) A logarithmic increase of the radius; (2) the systematic use of numerical fundamental solutions w of the Smoluchowski equation; (3) the use of polynomials of up to the 8