A BDF3 and new nonlinear fourth-order difference scheme for the generalized viscous Burgersequation

This study explores a third-order backward differentiation formula (BDF3) and nonlinear fourthorder difference method (FODM) for solving the generalized viscous Burgers ' equation (GVBE). The BDF3 method is employed for discretizing the time derivative, while the nonlinear term u(lambda)u(chi)is handled using a newly constructed nonlinear fourth-order difference operator. The spatial second derivative is discretized using a linear fourth-order difference formula. We establish the convergence of the proposed BDF3-FODM by introducing a cut-off function (COF). The main contributions include the construction of a novel nonlinear fourth-order difference operator, addressing the limitation observed in Zhang et al. (2021), Guo et al. (2023), where the order of spatial convergence was restricted to second order. Finally, a numerical test is presented to validate our theoretical analysis.