High-order Difference Schemes For The Fourth-order Fractional Sub-diffusion Equations With Variable Coefficient

In this thesis,we study the numerical algorithms of a class of time fractional diffusion equations with variable coefficient and fourth order space derivatives under the two different boundary conditions.The thesis is consisted with two parts.In the first part,two difference schemes with second order time accuracy are obtained by using L2-1? and FL2-1? formula respectively to discretize the Caputo time fractional derivative under the first Dirichlet boundary conditions.The solvability,unconditional stability and convergence of the schemes are strictly proved by means of the discrete energy method and the mathematical induction method.Numerical results are consistent with theoretical analysis and the FL2-1? scheme can improve the calculation efficiency significantly.In the second part,two difference schemes subject to the second Dirichlet boundary con-ditions of the equations are constructed.The energy method and the mathematical induc-tion method are used to analyze the difference schemes.The numerical results show that the schemes have second order time convergence.Compared with L2-1? scheme,the computation of FL2-1? scheme is much faster.