This paper is devoted to construct approximations of the probability density function of the non-autonomous first-order homogeneous linear random differential equation, where the initial condition and the diffusion coefficient 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.
Journal of Computational and Applied Mathematics – Elsevier
Published: Aug 1, 2018
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