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} $ tau <= Ch1/s, where h and tau are mesh size and time step, respectively, the positive constant C is independent of h, and $ s=1,\ldots, 5 $ s=1,& mldr;,5 is the order of the IMEX-BDF method. Numerical experiments are also presented to verify the accuracy of the considered schemes.