A stencil of the finite-difference method for the 2D convection diffusion equation and its new iterative scheme

Abstract

The paper gives the numerical stencil for the two-dimensional convection diffusion equation and the technique of elimination, and builds up the new iterative scheme to solve the implicit difference equation. The scheme's convergence and its higher rate of convergence than the Jacobi iteration are proved. And the numerical example indicates that the new scheme has the same parallelism and a higher rate of convergence than the Jacobi iteration.

Keywords:

• convection diffusion equation
• finite difference
• iterative method
• mathematics stencil
• parallelism

2000 AMS Subject Classifications :

• 65M06
• 65M12
• 65Y05

Acknowledgements

This work was supported by NSF of China (10671113) and Shandong province (Y2003A04).