A Numerical Scheme Based on FD-RBF to Solve Fractional-Diffusion Inverse Heat Conduction Problems

Abstract

In this paper we investigated a fractional-diffusion inverse heat conduction problem (FIHCP). The numerical computation of fractional derivatives from noisy data is a typical ill-posed problem. Based on the fractional derivative of radial basis functions (RBFs), we proposed an effective numerical scheme to alleviate the difficulty of the ill-posed FIHCP. To demonstrate the efficiency and stability of the proposed scheme, we provide some theoretical analysis and numerical results of the proposed method.