MARIA GROPPI

Un metodo numerico-stocastico per equazioni scalari di reazione-diffusione

Pages 315-324
Received: 29 December 1995  
AMS Classification: 35K57

Abstract A probabilistic method of "gradient random walk" type to solve reaction diffusion equation is presented. The method is based on the strong connection between partial differential equations of parabolic type and stochastic differential equations. It is a fractional step method, with both steps of tochastic type: a random walk is combined with creation and destruction of elements. The probabilistic interpretation is emphasized and a rigorous derivation of the random walk as solution of a stochastic differential equation is deduced.