Numerical simulation for certain stochastic ordinary differential equations (Q1082047)

A Monte Carlo simulation approach is presented for solving two problems based on stochastic ordinary differential equations, namely an initial- value problem for a nonlinear ordinary differential equation and a two- point boundary-value problem for a linear equation. The method consists of simulating on the computer several realizations of the random process which appears in the coefficients of the equations, and then computing the average over the corresponding solutions. Since these two problems are related to the same physical problem, we are able to compare the results. Several plots are given to illustrate the results and a discussion of the various kinds of errors which affect the method is presented.