The Study Of Discrete For Fractional-in-time Fourth-order Diffusion Equations On Nonuniform Time-steps

In this article,finite difference method is applied to study the fourth-order subdiffusion e-quation on nonuniform time-steps.The fourth-order problem is reduced into a couple of spatially second-order system.Two compact finite difference schemes are proposed by use an averaged op-erator to construct a fourth-order spatial approximation.The L1 formula formula on irregular mesh are considered for the Caputo fractional derivative in the first scheme.The Alikhanov formula on nonuniform meshes are considered for the Caputo fractional derivative in the second scheme.Be-sides,we can resolve the initial singularity of solution by putting more grid points near the initial time.The stability and convergence are established by using three theoretical tools:a complemen-tary discrete convolution kernel,a discrete fractional Gronwall inequality and an error convolution structure.Some numerical experiments are reported to demonstrate the accuracy and efficiency of our method.