Abstract

Based on the exponent transform to eliminate the ``convection item'' in the equation and the fourth-order compact difference formulas for the first and second derivatives, two chasses of new implicit difference schemes are proposed for solving the one-dimensional convection-diffusion equation. The methods are of order $O\left(
{\tau ^2 + h^4} \right)$ and $O\left( {\tau ^4 + h^4} \right)$ respectively. The former is proved to be unconditionally stable while the later is unconditionally unstable by Fourier analysis. The result of numerical experiment shows that the $O\left( {\tau ^2 + h^4} \right)$ scheme is an effective difference scheme to solve the convection diffusion problem.

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