Complexity of Monte Carlo Method in Application to Fredholm Integral Equations of the Second Kind

This paper is intended to provide a numerical algorithm consisted of the combined use of the trapezoidal rule and Monte Carlo method to solve Fredholm integral equations of the second kind. The numerical method is based on the discretized integral equation by trapezoidal rule. Owing to the application of the trapezoidal rule, a system of linear algebraic equations is obtained. An approach of Monte Carlo method is employed to solve the linear system. Numerical tests are performed in order to show the efficiency and accuracy of the present work.