A new difference scheme with high accuracy and absolute stability for solving convection–diffusion equations

In this paper, we use a semi-discrete and a padé approximation method to propose a new difference scheme for solving convection–diffusion problems. The truncation error of the difference scheme is O ( h 4 + τ 5 ) . It is shown through analysis that the scheme is unconditionally stable. Numerical experiments are conducted to test its high accuracy and to compare it with Crank–Nicolson method.