A stable numerical scheme for a time fractional inverse parabolic equation

作者：Taghavi A^*; Babaei A; Mohammadpour A

来源：Inverse Problems in Science and Engineering, 2017, 25(10): 1474-1491.

DOI：10.1080/17415977.2016.1267169

• Caputo fractional derivatives
• time fractional inverse problem
• finite differences
• Tikhonov regularization method
• discrepancy principle

In this paper, we consider a time fractional inverse heat conduction problem of finding the temperature distribution and the heat flux on the boundary , 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 pointand the given heat flux on the boundary 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.

• 出版日期2017