A. GOLBABAI ET AL.1467

Figure 10. Distribution of eigen-values in BLAGE precon-

ditioner.

5. Conclusions

A high-order compact scheme in combination precondi-

tioner was applied successfully to Diffusion- Convection

equation. We study comparison of different precondi-

tioners in combination Krylov subspace methods. High-

order approximation are designed by the need to produce

more stable schemes which are efficient with respect to

the operation number and that do not experience difficul-

ties near boundaries. The numerical results which is given

in the previous section d emonstrate the good accuracy of

this scheme and efficiency of preconditioned Krylov sub-

space methods. We got to this conclusion that the ADI

preconditioner is effective for model problems rather

than other. So we propose using ADI preconditioner in

combination with Krylov subspace methods for solving

non-symmetric systems because this preconditioner needs

to less computing time and have the less iteration number

than other. Also, we propose the BiCGSTAB method

because of the need to less iteration number, simplicity

in implementation, flat convergence and to save in comp

tational time.

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