Numerical integral transform methods for random hyperbolic models

Abstract

[EN] This work deals with the construction of analytic-numerical solutions, in the mean square sense of the random heterogeneous telegraph type problem. Efficient methods for solving numerically deterministic problems such as finite-difference methods become unsuitable for the random case because of the computation of the expectation and the variance of the approximation solution s.p. The drawbacks are essentially of computational complexity such as the handling of big random matrices which appear throughout the iterative levels of the discretization steps and the necessity to store the information of all the previous levels of the iteration process. Then, they motive the search of non iterative alternatives. In this sense, this paper provides an approximation solution s.p. of the problem (1) (4) which combines the random Fourier sine transform, the Gauss-Laguerre quadrature rule and the Monte Carlo method.