Solving initial value problem of ordinary differential equations by Monte Carlo method

Monte Carlo method was a new numerical method different from traditional method. It was based on probability and statistics theory, so it was also called as random sampling or statistical test method. In this paper, on the basis of Monte Carlo method, a new way to solve initial value problem of ordinary differential equations was presented. The authors have given the calculating process in detail. Some calculation samples, such as one-order ordinary differential equations, implicit second order differential equation and Vander Pol equation, showed the exactitude and efficiency of the method. And all the relative errors were less than 1%.