Numerical Solution of the One-Dimensional General Diffusion Equation

The general diffusion equation is equivalent to the Fokker-Planck equation and it also appears when expressing the standard diffusion equation in another coordinate system by a non-linear transformation, e.g. in phase-space variable transformations. We establish a reliable algorithm solving this equation for any possible case, and realize it in a computer program. When applied to cases where analytical solutions are known, this program gives results which are in excellent agreement with these.