Two Classes Locally One-dimension Method For Two Dimension Fractional Diffusion Equation

Fractional diffusion equation is a class of important fractional differential equation.Specially,more practical significance have been given to the two-dimension fractional differential equation.In recent years,a lot of numerical methods have been proposed to solve the fractional differential equation.For example,the alternating direction implicit schemes and the locally one-dimension method.These two methods are both fractional steps method and they all have advantages of concise format and less amount of computation.In view of these advantages,more and more experts all over the world have been engaged in the research of these methods and many papers about it have been published.In this paper,we will research the locally one-dimension method for two-dimension fractional diffusion equation.In section l,we briefly introduce the fractional diffusion eq-uation as well as the works made by experts and then the summary of this work has been given.In section2,we propose a unconditionally stable locally one-dimension difference s-cheme by adding infinitesimal item and the truncation error of the scheme are given.In a-ddition, the unconditional stability and error analysis of the scheme are proved by fourier method.In section3,we propose a high-accuracy locally one-dimension difference scheme b-y adding another infinitesimal item and the truncation error of the scheme are given.Co-mpared with former, this scheme has higher accuracy.In addition, the stability and error a nalysis of the scheme are proved by fourier method.In section4,we verify the accuracy of these two schemes proposed in section3and section4by using two examples.