Numerical solutions of random integral equation III: random Chebyshev polynomials and Fredholm equations of the second kind ∗

We consider, in this article, a numerical study of a certain class of Singular Cauchy integral equations with random nonhomogeneous term. The method is based on an approximation of the solution by random Chebyshev polynomials. Numerical results, based on simulation, of random forcing term are given and they are used (i) to determine the distribution of the random coefficients of the Chebyshev polynomial and (ii) to compare the mean of the random solution with the solution of the mean equation (which of course is deterministic)