A New Numerical Method for Solving Convection-Diffusion Equations

In this paper, we using semi-discrete method, transformed convection-diffusion equation into a ODEs: \(\frac{dU(t)}{dt}\) = AU(t), then we get the solution of the ODEs: U(t) = e tA U0. Furthermore, we give a numerical approximation for e tA and get a special difference scheme for solving the convection-diffusion equation which improve the accuracy order and stability condition greatly. The accuracy order is fourth order and second order in space and time direction respectively. Finally, numerical result shows that this method is effective.