Some Notes on Numerical Convergence of the Stochastic Perturbation Method

摘要

This paper concerns numerical convergence studies of the general n-th order stochastic perturbation technique applied frequently to randomize some boundary value of boundary initial problems in computational mathematics as well as to additionally modify numerical methods in engineering. The general scheme of the technique is introduced and invented in terms of the coupled viscous fluid dynamics problem. Symbolic mathematics package MAPLE and its visualization tools are engaged to perform computational studies on convergence of the first two probabilistic moments for the simple unidirectional Couette Newtonian fluid flow. The methodology and its implementations need many further improvements, however their efficient applications in various engineering problems are possible now.