Pointwise error estimates of compact difference scheme for mixed-type time-fractional Burgers’ equation

In this paper, based on the developed nonlinear fourth-order operator and method of order reduction, a novel compact difference scheme is constructed for mixed-type time-fractional Burgers’ equation, from which L1-discretization formula applied to deal with terms fractional derivative, convection term discretized by operator. Then fully discrete L1 uniform meshes can be established approximating spatial second-order derivative classic formula. The convergence stability proposed are rigorously proved in L?-norm energy argument mathematical induction. We also establish temporal graded time solving problem weak initial singularity. Finally, several numerical experiments provided test accuracy two schemes verify theoretical analysis.