A Dufort-Frankel scheme for one-dimensional uncertain heat equation

Abstract

Abstract Uncertain heat equation (for short, UHE) is a type of second-order uncertain PDEs driven by Liu processes. In most cases, since it is tough to get the analytic solution for a UHE, we must find a way to obtain its numerical solution. A forward difference scheme has been designed to solve UHE, but our paper will show that this method may exhibit instability in some situations. We explore another approach, unconditionally stable and namely Dufort-Frankel method. Moreover, this paper will use Dufort-Frankel method to calculate the expected value and extreme value of the solution for a UHE.