Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme

Abstract

Numerical solution and parameter estimation for a type of fractional diffusion equation are considered. Firstly, the symmetrical compact difference scheme is applied to solve the forward problem of the fractional diffusion equation. The stability and convergence of the symmetrical difference scheme are presented. Then, the Bayesian method is considered to estimate the unknown fractional order α of the fractional diffusion equation model. To validate the efficiency of the symmetrical numerical scheme and the estimation method, some simulation tests are considered. The simulation results demonstrate the accuracy of the compact difference scheme and show that the proposed estimation algorithm can provide effective statistical characteristics of the parameter.