CERTAIN PROBLEMS WITH THE APPLICATION OF STOCHASTIC DIFFUSION-PROCESSES FOR THE DESCRIPTION OF CHEMICAL-ENGINEERING PHENOMENA - NUMERICAL-SIMULATION OF ONE-DIMENSIONAL DIFFUSION PROCESS

Some problems are analyzed arising when a numerical simulation of a ra ndom motion of a large ensemble of diffusing particles is used to appr oximate the solution of a one-dimensional diffusion equation. The part icle motion is described by means of a stochastic differential equatio n. The problems emerging especially when the diffusion coefficient is a function of spatial coordinate are discussed. The possibility of sim ulation of various kinds of stochastic integral is demonstrated. It is shown that the application of standard numerical procedures commonly adopted for ordinary differential equations may lead to erroneous resu lts when used for solution of stochastic differential equations. Gener al conclusions are verified by numerical solution of three stochastic differential equations with different forms of the diffusion coefficie nt.