Numerical Algorithm For A Class Of Time Fractional Diffusion Equations With Local Memory

In this paper,we consider a class of time fractional diffusion equations with local memory.For the equivalent form of the equation,we establish one and t-wo dimensional fully discrete time-space schemes for the equivalent form of the equation.In the time direction,backward difference and L₁ method are used.In space,the compact difference operator is used to discretize the Laplace operator.We also analyze the stability and convergence of time semi-discrete lattices,one-and two-dimensional fully discrete schemes.Finally,numerical experiments veri-fy the convergence conclusion that the time step has first-order accuracy and the space step has fourth-order accuracy in the numerical format.