Identification Of Convection Term For Space-time Fractional Convection-diffusion Equation

We always study the classic convection-diffusion equation(the integer or-der convection-diffusion equation)and know the class of problem well.However,the classic convection-diffusion equation is not usually used to simulate some phe-nomena in our life,especially to abnormal phenomena,so fractional convection-diffusion equation is raised.Now its form is as follows:To solve this class of equation,its numerical method is similar to the classic convection-diffusion equation’s,but it relates to Caputo fractional order deriva-tive and Riemann-Liouville fractional order derivative respectively before we disperse the time fractional order and space fractional order.After we get the dispersed equation group,we use the fast algorithm to solve this equation group to reduce the compute time and the storage space.In addition, we often encounter the inverse problem of the type of model: when observations uO,uT is known, but some coefficients of the model a(x), b(x), c(x), q(x, t) may be also unknown.We main use Gradient regularization method to solve this type of problem.In this article,we are going to study the situation that the coefficient of the conviction term-a(x) is unknown,which requires the solution of<u{x. t), a(x)>.The article is organized as follows:The first chapter is some prior knowl-edge:introducing the actual meaning of space-time fractional equation,the knowledge of inverse problem,gradient regularization method and fast algo-rithm;The second chapter gives the explicit scheme of space-time fractional equation and the analysis of its stability and convergence;In the third chap-ter,we give the implicit scheme of space-time fractional equation and the anal-ysis of its stability and convergenee;We mainly introduce the identification of the convection term’s coefficient in the forth chapter;The fifth chapter gives a specific numerical example to achieve the purpose of inspection on the above analysis.