关于抛物型方程问题蒙特卡罗方法的一点注记

MONTE CARLO METHOD FOR SOLVING A TYPICAL PROBLEM OF PARABOLIC DIFFERENTIAL EQUATION

摘要: 本文企图把适用于固定边界的定常边界条件的热传导方程的蒙特卡罗方法,推广到变动边界的不定常边界条件的热传导方程中去。本文讨论的问题虽然只是三个独立变量的问题,但不难将其推广,使适用于更高维数的方程。

Abstract: In this paper the writer presents a Monte Carlo solution of the difference equation corresponding to the parabolic partial differential equation （?）u/（?）t=a²△u（x,y,t）, （x,y,t）∈D under boundary condition u（x,y,t）=f（x,y,t）, （x,y,t）∈r and initial condition u（x,y.0）=g（x,y）. The method is described as a two-dimensional random walk.