Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar

Abstract

This paper deals with the analytic-numerical solution of random heat problems for the temperature distribution in a semi-infinite bar with different boundary value conditions. We apply a random Fourier sine and cosine transform mean square approach. Random operational mean square calculus is developed for the introduced transforms. Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. Then, expectation and variance are computed. Illustrative numerical examples are included.