Using the Monte Carlo method to solve integral equations using a modified control variate

摘要

One of the numerical methods for solving definite integrals is Monte Carlo (MC) randomized simulation. In this paper we intend to apply a Monte Carlo variance reduction technique to solve the linear Fredholm integral equations, which is based on a modified control variate. Taylor expansion to each subinterval of the objective function is regarded as the modified control variate. And thus we solve the linear Fredholm integral equations of the second kind more accurately. One of the main advantage of the proposed method is reducing the problem caused by the linear system of equations.