RBFs Algorithm For Variable Order Fractional Equation

Recently the field of the variable order time fractional equation has been widely attentted.It has important applications in many fields,beacuse of the complex of its exact solution,it makes more people get into the numerical solu-tion’s research.In this paper,we discuss the numerical simulation of the variable order time fractional equation under the Coimbra definition using radical basis functions.Radial basis function (RBF) plays an important role in differential equation, and it is gradually applied in the solution of the fractional order dif-ferential equation, and MQ function is an important radial basis function.This paper uses inverse MQ function interpolation method, discusses a numerical method of time fractional diffusion equation, specific contents are arranged as following:In chapter one,we make a comprehensive elaboration and introduces the developing process of the variable order time fractional equation and known numerical solutions.In chapter two,we give the related preparatory knowledge, simply intro-duce the basic theory and radial basis function interpolation, and specially in-troduce the MQ function and inverse MQ function interpolation theory, make preparation for the follow-up work.In chapter three, we introduce a kind of numerical algorithm about vari-able time fractional diffusion equation by Dr Shen, and introduce the stability and convergence of the method.The chapter four is the core content of this paper, using inverse MQ function interpolation to study numerical solution of the variable order time fractional diffusion equations, we propose an adaptive least-squares collocation radial basis function method,and discusse the stability and conergence of th algorithm.In chapter live,we use a munerical example to verify the feasibility and effectiveness of this algorithm,then calculate the error of the algorithm.Finally we elaborate the conclusions and outlook of this paper,and put forward a preliminary opinion on future work.