Multistep finite difference schemes for the variable coefficient delay parabolic equations

作者：Zhang, Qifeng; Li, Dongfang^*; Zhang, Chengjian; Xu, Dinghua

来源：Journal of Difference Equations and Applications, 2016, 22(6): 745-765.

DOI：10.1080/10236198.2016.1142539

• Variable coefficient delay parabolic differential equations
• multistep finite difference scheme
• ADI scheme
• solvability
• stability
• convergence

In this paper, we study the high efficient numerical methods to solve a class of variable coefficient delay parabolic differential equations. We propose two types of multistep finite difference schemes while prove the solvability, convergence and stability of both schemes. The convergence orders are O(tau(2) + h(2)) and O(tau(2) + h(4)), respectively, in the sense of L-infinity-norm. By some new analytical transformations, we extend our schemes to solve a more general variable coefficient delay convection-diffusion-reaction equations and also apply them to the higher dimensional cases. Furthermore, multistep finite difference method and compact multistep finite difference method for two dimensional variable coefficient diffusion-reaction equations are proposed and the suitable alternate direction implicit (ADI) technique is constructed for the multistep finite difference scheme. At last, several numerical experiments are carried out to illustrate the effectiveness of both schemes.

• 出版日期2016
• 单位华中科技大学; 浙江理工大学