  We describe an exact and highly efficient numerical algorithm for solving a
special but important class of convection-diffusion equations. These equations
occur in many problems in physics, chemistry, or biology, and they are usually
hard to treat due to the presence of a convection term, represented by a first
order derivative in the spatial co-ordinate. Our algorithm reduces the
convection-diffusion equation to a pure diffusion problem within a
complex-valued potential which can be solved efficiently and accurately using
conventional parabolic partial differential equation solvers.
