A spectral Galerkin method for nonlinear delay convection-diffusion-reaction equations

作者：Liu Bochao; Zhang Chengjian^*

来源：Computers & Mathematics with Applications, 2015, 69(8): 709-724.

DOI：10.1016/j.camwa.2015.02.027

• Spectral Galerkin methods
• Stability
• Convergence
• Nonlinear delay convection-diffusion-reaction equations
• Crank-Nicolson scheme

This paper deals with the numerical approximation of a class of nonlinear delay convection-diffusion-reaction equations. In order to derive an efficient numerical scheme to solve the equations, we first convert the original equation into an equivalent reaction-diffusion problem with an exponential transformation. Then, we propose a fully discrete scheme by combining the Crank-Nicolson method and the Legendre spectral Galerkin method. The analytical and numerical stability criteria are obtained in L-2-norm. It is proven under the suitable conditions that the method is convergent of second-order in time and of exponential order in space. Finally, several numerical experiments are given to illustrate the computational efficiency and the theoretical results.

• 出版日期2015-4
• 单位华中科技大学