A note on convergence of line iterative methods for a nine-point matrix (Q1861794)
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scientific article; zbMATH DE number 1878880
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on convergence of line iterative methods for a nine-point matrix |
scientific article; zbMATH DE number 1878880 |
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A note on convergence of line iterative methods for a nine-point matrix (English)
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10 March 2003
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The authors consider the special convection-diffusion equation, \(-\varepsilon\Delta u+u_x=f\), with unit convection velocity parallel to the \(x\)-coordinate direction. The domain of interest is the unit square and the equation is discretized with uniform square mesh elements with side length \(h\). The critical parameter is the so-called cell Reynolds number \(\gamma=h/(2\varepsilon)\). The authors employ a fourth order difference scheme due to \textit{M. M. Gupta, R. P. Manohar} and \textit{J. W. Stephenson} [Numerical properties and methodologies in heat transfer, Proc. 2nd nat. Symp., College Park, Md. 1981, 201-209 (1983; Zbl 0515.76097)].
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convection diffusion equation
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fourth order compact scheme
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line Jacobi method
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line Gauss-Seidel method
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convergence
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line iterative methods
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difference scheme
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