Stochastic dynamic approach to transport phenomena

A stochastic dynamic approach to the equations of change is introduced here, which first is applied to linear equations and is based on the formal analogy between certain forms of the equations of change and the Fokker-Planck equation. A stochastic differential equation associated with the Fokker-Planck equation can be derived from the latter and solved numerically, thus yielding the solution to the original equation of change. The proper treatment of boundary conditions is essential for the success of the method. We show that the method is able to handle the eight fundamental types of boundary conditions (Carslaw and Jaeger, 1959; Crank, 1975). In addition, the stochastic dynamic approach provides a deeper insight in the physical processes underlying transport phenomena than do traditional techniques.