An Implicit Finite Difference Scheme with Preconditioning for Convection Dominated Diffusion Equation
An implicit finite difference scheme for solving time-dependent convection dominated diffusion equations in two space variables is presented. A one-sided difference approximation is used for the convection terms and a second-order central difference approximation for the diffusion term. The implicit scheme is consistent, unconditionally stable and itpsilas L2 error estimation is optimal. By preconditioning technique of incremental unknowns, the implicit scheme is an efficient one.
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