Abstract: This paper introduces three random walk models on computating parabolic equations solved by Monte Carlo method, the corresponding prove and the error estimation are given; then a method on computating parabolic functions parallel is proposed based on the combination of Monte Carlo method with domain decomposition algorithm, the algorithm for onedimension functions is expounded. The condition suitable to the algorithm is given. Some numerical experiments were carried out for 2Dand 3Dparabolic functions. The resultsshow that the method can well handle parabolic functions parallel and can save lots of time.

Key words: Monte Carlo method, domain decomposition, parallel computation, parabolic equation