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Two-step iterative methods for solving the stationary convection-diffusion equation with a small parameter at the highest derivative on a uniform grid. (Russian, English) Zbl 1210.39018

Zh. Vychisl. Mat. Mat. Fiz. 46, No. 2, 295-306 (2006); translation in Comput. Math. Math. Phys. 46, No. 2, 282-293 (2006).
Summary: A stationary convection-diffusion problem with a small parameter multiplying the highest derivative is considered. The problem is discretized on a uniform rectangular grid by the central-difference scheme. A new class of two-step iterative methods for solving this problem is proposed and investigated. The convergence of the methods is proved, optimal iterative methods are chosen, and the rate of convergence is estimated. Numerical results are presented that show the high efficiency of the methods.

MSC:

39B12 Iteration theory, iterative and composite equations
65F10 Iterative numerical methods for linear systems
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