Computing the probability density function of non-autonomous first-order linear homogeneous differential equations with uncertainty

[EN] This paper is devoted to construct approximations of the probability density function of the non-autonomous first-order homogeneous linear random diff erential equation, where the initial condition and the diff usion coe fficient are assumed to be a random variable and a stochastic process, respectively. We combine Random Variable Transformation technique and Karhunen-Loève expansion to construct reliable approximations under general conditions. Several numerical examples illustrate our theoretical findings.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2017-89664-P. Ana Navarro Quiles acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2018). Computing the probability density function of non-autonomous first-order linear homogeneous differential equations with uncertainty. Journal of Computational and Applied Mathematics. 337:190-208. https://doi.org/10.1016/j.cam.2018.01.01519020833