Local discontinuous Galerkin methods with implicit–explicit BDF time marching for Newell–Whitehead–Segel equations.

The Newell–Whitehead–Segel type equations with time-dependent Dirichlet boundary conditions are solved by the local discontinuous Galerkin (LDG) method coupled with the implicit–explicit backward difference formulas (IMEX-BDF). With a suitable setting of numerical fluxes and by the aid of the multiplier technique and the a priori error assumption technique, the optimal error estimate for the corresponding fully discrete LDG-IMEX-BDF schemes is obtained by energy analysis, under the condition $ \tau \le C h^{1/s} $ τ≤Ch1/s, where <italic>h</italic> and <italic>τ</italic> are mesh size and time step, respectively, the positive constant <italic>C</italic> is independent of <italic>h</italic>, and $ s=1,\ldots, 5 $ s=1,…,5 is the order of the IMEX-BDF method. Numerical experiments are also presented to verify the accuracy of the considered schemes. [ABSTRACT FROM AUTHOR]