Numerical solution of integral equations with Monte Carlo-collocation (MC-Coll) method and its application in neutron transport

Abstract

In this study, we introduce a new procedure for the numerical solution of linear and nonlinear integral equations by combining the Monte Carlo simulation and collocation method. One of the major advantages of this method is reducing calculations by converting the integral equation to a system of algebraic equations. The numerical examples of various types of integral equations indicate the efficiency and accuracy of the proposed method. The results show this method is able to solve linear and nonlinear integral equations and also nonlinear weakly singular equations, with remarkable accuracy. Finally, the method is generalized for solving integral-differential equation of the neutron transport for the stationary case.