The quasi-boundary value regularization method for identifying the initial value with discrete random noise

Abstract

Abstract In this paper, we study an inverse initial value problem for the fractional diffusion equation with discrete noise. This problem is ill-posed in the sense of Hadamard. We apply the trigonometric method in a nonparametric regression associated with the quasi-boundary value regularization method to deal with this ill-posed problem. The corresponding convergence estimate for this method is obtained. The numerical results show that this regularization method is flexible and stable.

Keywords

• Time-fractional diffusion equation
• Quasi-boundary value regularization method
• Nonparametric regression
• Discrete random data