1. A fourth-order method of the convection–diffusion equations with Neumann boundary conditions
- Author
-
Cao, Huai-Huo, Liu, Li-Bin, Zhang, Yong, and Fu, Sheng-mao
- Subjects
- *
NUMERICAL solutions to parabolic differential equations , *BOUNDARY value problems , *MATHEMATICAL physics , *FINITE differences , *DISCRETE ordinates method in transport theory , *NUMERICAL analysis , *APPROXIMATION theory , *LINEAR differential equations - Abstract
Abstract: In this paper, we have developed a fourth-order compact finite difference scheme for solving the convection–diffusion equation with Neumann boundary conditions. Firstly, we apply the compact finite difference scheme of fourth-order to discrete spatial derivatives at the interior points. Then, we present a new compact finite difference scheme for the boundary points, which is also fourth-order accurate. Finally, we use a Padé approximation method for the resulting linear system of ordinary differential equations. The presented scheme has fifth-order accuracy in the time direction and fourth-order accuracy in the space direction. It is shown through analysis that the scheme is unconditionally stable. Numerical results show that the compact finite difference scheme gives an efficient method for solving the convection–diffusion equations with Neumann boundary conditions. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF