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

ABSTRACT

In 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 $L^2$-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.

KEYWORDS:

• Delay convection-diffusion-reaction equations
• implicit–explicit multistep methods
• finite-element method
• error estimate
• stability

2010 AMS SUBJECT CLASSIFICATION:

• 35R10
• 65L06
• 65M60
• 65M12

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11701110, 11671343, 11501485), and Program on the High Level Innovation Team and Outstanding Scholars in Universities of Guangxi Province.