Solving the random Legendre differential equation: Mean square power series solution and its statistical functions

In this paper we construct, by means of random power series, the solution of second order linear differential equations of Legendre-type containing uncertainty through its coefficients and initial conditions. By assuming appropriate hypotheses on the data, we prove that the constructed random power series solution is mean square convergent. In addition, the main statistical functions of the approximate solution stochastic process generated by truncation of the exact power series solution are given. Finally, we apply the proposed method to some illustrative examples to compare the numerical results for the average and the variance with respect to those obtained by the Monte Carlo approach. © 2011 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universidad Politecnica de Valencia grant PAID06-09-2588 and Mexican Conacyt.Calbo Sanjuán, G.; Cortés López, JC.; Jódar Sánchez, LA.; Villafuerte Altuzar, L. (2011). Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Computers and Mathematics with Applications. 61(9):2782-2792. doi:10.1016/j.camwa.2011.03.045S2782279261