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

@article{Song2010AMC,
  title={A modified Crank-Nicolson scheme with incremental unknowns for convection dominated diffusion equations},
  author={Lunji Song and Yujiang Wu},
  journal={Appl. Math. Comput.},
  year={2010},
  volume={215},
  pages={3293-3301}
}
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 L^2 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… Expand
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