Quasi-Monte Carlo Method via a Numerical Algorithm to Solve Fredholm Integral Equations of the Second Kind

This paper is intended to provide a numerical algorithm involving the combined use of the successive substitution method and quasi-Monte Carlo method for the solution of Fredholm integral equations of the second kind. Owing to the application of the successive substitution method a series of multiple integrals is obtained. An approach of quasi-Monte Carlo method is employed to solve the multiple integrals. Numerical tests are performed in order to show the efficiency and accuracy of the present work.