@misc{10481/96032,
year = {2020},
month = {5},
url = {https://hdl.handle.net/10481/96032},
abstract = {We study the random heat partial differential equation on a bounded domain assuming that the diffusion coefficient and the boundary conditions are random variables, and the initial condition is a stochastic process. Under general conditions, this stochastic system possesses a unique solution stochastic process in the almost sure and mean square senses. To quantify the uncertainty for this solution process, the computation of the probability density function is a major goal. By using a random finite difference scheme, we approximate the stochastic solution at each point by a sequence of random variables, whose probability density functions are computable, i.e., we construct a sequence of approximating density functions. We include numerical experiments to illustrate the applicability of our method.},
organization = {Ministerio de Economía y Competitividad},
keywords = {Random heat partial differential equation},
keywords = {Probability density function},
keywords = {Numerical method},
keywords = {Uncertainty quantification},
keywords = {Finite difference scheme},
title = {Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme},
doi = {10.1016/j.apnum.2020.01.012},
author = {Calatayud, Julia and Cortés, Juan Carlos and Díaz Navas, José Antonio and Jornet, Marc},
}