A stable numerical scheme for a time fractional inverse parabolic equation

In this paper, we consider a time fractional inverse heat conduction problem of finding the temperature distribution and the heat flux on the boundary x=0, when the time fractional derivative is interpreted in the sense of Caputo. We prove that this problem is an ill-posed problem. For finding a stable solution, the Tikhonov regularization technique is applied. A finite difference scheme is considered by using the given temperature at a point x=x∗,0<x∗<1 and the given heat flux on the boundary x=1. Stability analysis by using the Von Neumann (or Fourier) method and convergence are discussed. Numerical examples show that the proposed method is stable and works well.