Efficient third-order BDF finite difference scheme for the generalized viscous Burgers’ equation

This article presents a third-order backward differentiation formula (BDF3) finite difference scheme for the generalized viscous Burgers’ equation. The discretization of time and space directions is accomplished by the BDF3 method and standard second-order difference formula, respectively, thereby constructing a fully-discrete scheme. For the proposed scheme, we yield the convergence of h2+τ3 by means of the energy argument and the cut-off function method. Besides, a comparison of the time convergence rate and numerical accuracy with those of recent existing work shows the effectiveness and competitiveness of our approach. A numerical experiment is carried out to verify the theoretical predictions.