EI and IE difference schemes and numerical simulation for time fractional convection-diffusion equation

• 1、Mathematics and Physics Department, North China Electric Power University, Beijing 102206

Abstract：Time fractional convection-diffusion problem is not only an important physical issue,but also a practical issue generally involved in engineering. For the time fractional convection-diffusion equation, this paper combines classical explicit scheme and classical implicit scheme, and constructs a class of numerical difference schemes- Explicit Implicit (EI) difference scheme and Implicit Explicit (IE) difference scheme. The theoretical analyses prove the unique solvability, the stability and convergence for the numerical solutions of EI and IE difference schemes, and prove that EI and IE schemes have 2-order spatial accuracy and 2-α-order temporal accuracy. Numerical experiments verify the theoretical analyses, which shows that EI and IE difference methods are time-saving and the computational time is reduced by about 28% compared with that of the classical implicit scheme under the similar computational accuracy. All above show that EI and IE schemes are feasible to solve the time fractional convection-diffusion equation.

Keywords： Time fractional convection-diffusion equation Explicit Implicit (EI) and Implicit Explicit (IE) difference scheme Stability Convergence order Numerical experiments