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Integral equations are often involved in the mathematical formulation of physical phenomena, they can be encountered in various fields of science, such as the heat radiation problems. Fredholm integral equations for 1-D backward heat conduction problems were studied in [1]. There are many methods to obtain the solution of an integral equation, such as the meshless method [2], the Legendre-Gauss-Lobatto collocation method [3], the piecewise linear maximum entropy method [4], etc. In this paper, it is our intention to numerically solve the Fredholm integral equation of the second kind by combining the classical Monte Carlo method and the Monte Carlo method with a control variate [5-8]. In this paper, we will consider the following Fredholm integral equation of the second kind: 1

Monte Carlo method with control variate for integral equations