Boundary functions determination in an inverse time fractional heat conduction problem

Abstract

In this study, we propose an effective approach for the numerically solution of a class of one-dimensional nonlinear inverse time fractional heat conduction problems. The boundary heat fluxes are considered as unknown functions of the boundary temperatures. A numerical method based on the finite difference and mollification approaches is developed to determine the unknown boundary functions. The stability and convergence of the numerical method are proved. Four test problems are conducted to illustrate the ability of the numerical algorithm.

Simulation of time-fractional oxygen diffusion in cornea coated by contact-lens

“…The left-hand side of Eq. ( 8) can be computed numerically in the following manner (Toubaei et al 2019):…”

“…( 8 ) can be computed numerically in the following manner (Toubaei et al. 2019 ): where is the time level indicator. refers to time step, and Discretizing the diffusion term in Eq.…”