Finite Difference/Spectral Approximations For A Class Of Anomalous Diffusion Equation

In this paper, a class of anomalous diffusion EQUATION through a combination of high-end finite difference scheme and the spatial spectrum method gives a high-precision discrete format, the format at the same time give details of the stability and convergence analysis paper mainlydivided into the following four parts.The first chapter introduces the research background, the historical development of fractional differential equations, this paper the use to the Riemann-Liouville definition and Caputo fractional derivative definitions and the relationships between them, and then put forward in this paper to study the anomalous diffusion equation and this paper gives a summary of work.The second chapter begins with the relationship between the Riemann-Liouville definition of Caputo defined fractional derivative according to Caputo defined discrete, integer-order derivative using second-order BDF discrete energy method, the semi-discrete system stabilityanalysis, proved to be unconditionally stable. On this basis, further given the convergence analysis of the semi-discrete format.The third chapter focuses on the discrete space. We apply the discrete spatial derivative of the Galerkin spectral method, to obtain a fully discrete format, using the projection properties of operators, given the spatial discretization error analysis. Finally, the conclusion of the second chapter gives the error analysis of fully discrete format.The fourth chapter gives a number of numerical experiments, numerical experiments to verify the effectiveness of the format, the algorithm is given derivation.