Non-Gaussian Quadrature Integral Transform Solution of Parabolic Models with a Finite Degree of Randomness

In this paper, we propose an integral transform method for the numerical solution of random mean square parabolic models, that makes manageable the computational complexity due to the storage of intermediate information when one applies iterative methods. By applying the random Laplace transform method combined with the use of Monte Carlo and numerical integration of the Laplace transform inversion, an easy expression of the approximating stochastic process allows the manageable computation of the statistical moments of the approximation.