An efficient explicit group method for time fractional Burgers equation - Salama, Fouad Mohammad (Frontiers in Physics, 2025)
Fractional Burgers-type equations are essential mathematical models for describing the cumulative effect of wall friction through the boundary layer, along with the unidirectional propagation of weakly nonlinear acoustic waves. It is a major challenge to develop efficient, stable, and accurate numerical schemes that simulate the corresponding complex physical phenomena due to the nonlinearity and nonlocality properties in these equations. The objective of this article is to design a linearized modified fractional explicit group method for solving the two-dimensional time-fractional Burgers equation with suitable initial and boundary conditions. For the construction of the proposed method, the L1 discretization formula is used to handle the fractional temporal derivative, whereas a linearized difference scheme on a coarse mesh is employed to approximate the spatial derivatives. Meanwhile, a linearized Crank–Nicolson difference method (LCNDM) is formulated for checking the efficiency of the proposed method. The stability and convergence of the presented methods are rigorously studied and proven. Numerical simulations are performed, and the results are reported in terms of error norm and CPU time, demonstrating that the linearized grouping method reduces computation time by 70%–90% while maintaining comparable accuracy to the linearized Crank–Nicolson method in solving the time-fractional Burgers model.