Monte Carlo simulation for solving Fredholm integral equations

Abstract

Purpose

The purpose of this paper is to provide a Monte Carlo variance reduction method based on Control variates to solve Fredholm integral equations of the second kind.

Design/methodology/approach

A numerical algorithm consisted of the combined use of the successive substitution method and Monte Carlo simulation is established for the solution of Fredholm integral equations of the second kind.

Findings

Owing to the application of the present method, the variance of the solution is reduced. Therefore, this method achieves several orders of magnitude improvement in accuracy over the conventional Monte Carlo method.

Practical implications

Numerical tests are performed in order to show the efficiency and accuracy of the present paper. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes CPU time at Pentium IV‐2.4 GHz PC.

Originality/value

This paper provides a new efficient method to solve Fredholm integral equations of the second kind and discusses basic advantages of the present method.

Citation

Farnoosh, R. and Morteza, E. (2009), "Monte Carlo simulation for solving Fredholm integral equations", Kybernetes, Vol. 38 No. 9, pp. 1621-1629. https://doi.org/10.1108/03684920910991577