Highly accurate method for the convection-diffusion equation

Abstract

In this paper, we shall develop a new approach to implicit method for solving the convection-diffusion equation, which will exhibit several advantageous features: highly accurate, fast and with good results whatever the exact solution is too large i.e., the absolute error still very small. The stability region is discussed and the obtained results for a test problem is compared with the exact solution and with Crank-Nicolson approximation, proves the mentioned advantages.

Keywords:

• Padé approximation
• restrictive Padé approximation
• exponential matrix
• convection-diffusion equation
• finite difference

1991 AMS Subject classification codes:

• 41A20
• 41A21
• 65M06

C.R. Categories:

• G.1.8