TVD Scheme For Fokker-Planck Equation

We study the TVD finite volume method for solving the following time fractional Fokker-Planck equation(FFPE)#12 where ??(0,1),ka is a positive constant,f(x)is a given function,and Dt1-??(x,t)is the Riemann-Liouville fractional derivative of order 1-?.In the TVD finite volume method,we use the TVD scheme and the central difference scheme to discretize the convection term and the diffusion term respectively,and use L1 scheme to discretize the time fractional derivative.We theoretically prove that the total variation in the method is not increasing and show the method is effective through numerical tests.Numerical test shows that when used to solve convectiondominated problems on relatively coarse space grid,our method has better stability and convergence.