A modified Crank–Nicolson scheme with incremental unknowns for convection dominated diffusion equations

A modified Crank–Nicolson scheme based on one-sided difference approximations is proposed for solving time-dependent convection dominated diffusion equations in two-dimensional space. The modified scheme is consistent and unconditionally stable. A priori L2L2 error estimate for the fully discrete modified scheme is derived. With the use of the incremental unknowns preconditioner at each time step, a comparison among several classical numerical schemes has been made and numerical results confirm stability and efficiency of the modified Crank–Nicolson scheme.