An implicit nonlinear difference scheme for two-dimensional time-fractional Burgers' equation with time delay

In this paper, based on the L1 discretization for the Caputo fractional derivative, a fully implicit nonlinear difference scheme with (2 - a)-th order accuracy in time and second-order accuracy in space is proposed to solve the two-dimensional time fractional Burgers' equation with time delay, where a ? (0,1) is the fractional order. The existence of the numerical scheme is studied by the Browder fixed point theorem. Furthermore, with the help of a fractional Gronwall inequality, the constructed scheme is verified to be unconditionally stable and convergent in L-2 norm by using the energy method. Finally, a numerical example is given to illustrate the correctness of our theoretical analysis.

Automated summary

In this paper, a fully implicit nonlinear difference scheme is proposed to solve the two-dimensional time fractional Burgers' equation with time delay based on the L1 discretization for the Caputo fractional derivative. The scheme has (2 - a)-th order accuracy in time and second-order accuracy in space, where a ? (0,1) is the fractional order. The existence of the numerical scheme is studied by the Browder fixed point theorem, and the unconditional stability and convergence of the scheme in L-2 norm are verified using the energy method and a fractional Gronwall inequality. A numerical example is also provided to illustrate the correctness of the theoretical analysis.