Implicit–explicit multistep finite-element methods for nonlinear convection-diffusion-reaction equations with time delay

ABSTRACTIn this paper, two classes of implicit–explicit (IMEX) multistep finite-element methods are constructed to solve the nonlinear delay convection-diffusion-reaction equations. This equations are discretized with finite-element method in space and IMEX multistep methods (including IMEX one-leg methods and IMEX linear multistep methods) in time. The resulting schemes are efficient because it can reduce the coupling degree, and avoid solving the large-scale systems of nonlinear algebraic equations. The L2-norm error estimates with handling the breaking point and stability results for the proposed methods are obtained. Numerical results demonstrate the efficiency and accuracy of the approaches.