A Truncation Method Based on Hermite Expansion for Unknown Source in Space Fractional Diffusion Equation

Abstract

In this paper we consider the problem for identifying an unknown steady source in a space fractional diffusion equation. A truncation method based on a Hermite function expansion is proposed, and the regularization parameter is chosen by a discrepancy principle. An error estimate between the exact solution and its approximation is given. A numerical implementation is discussed and corresponding results are presented to verify the effectiveness of the method.

Keywords:

• ill-posed problem
• unknown source
• truncation method
• Hermite functions expansion
• discrepancy principle

AMS Subject Classification:

• 65F22