Alternating group explicit method with exponential-type for the diffusion-convection equation

Based on the semi-explicit asymmetric exponential schemes constructed by the author, a new alternating group explicit (AGE) method with exponential-type for the numerical solution of the convection-diffusion equation is derived in the paper. The method has the obvious property of parallelism and is unconditionally stable. The results of numerical examples are given to show the effectiveness of the present methods that are in preference to the Evans and Abdullah' method in [Evans, D.J. and Abdullah, A.R., 1985, A new explicit method for the diffusion-convection equation. Computers & Mathematics with Application, 11, 145-154].