Geodesic
Accuracy of the numerical solution of the equations of diffusion-convection using the difference schemes of second and fourth order approximation error
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 1, pp. 47-62

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The paper deals with the scheme of the second and fourth order approximation error for solving convection-diffusion problems. To model initial boundary value problem in the case when the functions of the right and the initial condition can be represented by finite sums of Fourier series in the trigonometric basis, we investigated the accuracy of difference schemes. It was found that the accuracy of the numerical solution depends on the number of units attributable to half the wavelength corresponding to the most high frequency harmonics in the final sum of the Fourier series, necessary to describe the behavior of calculated objects. The dependence of the diffusion approximation error terms difference schemes of second and fourth order of accuracy of the number of nodes. The comparison of the calculation results of two-dimensional convection-diffusion problems and tasks of the Poisson-based schemes of the second and fourth order accuracy. In the expediency of transition to a scheme of high accuracy for solving applied problems of the estimates and is easy to obtain the numerical values of the gain in computation time by using schemes of higher order accuracy.
Keywords: accuracy difference schemes, approximation error.
Mots-clés : convection-diffusion equation 
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     title = {Accuracy of the numerical solution of the equations of diffusion-convection using the difference schemes of second and fourth order approximation error},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
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A. I. Sukhinov; A. E. Chistakov; M. V. Iakobovskii. Accuracy of the numerical solution of the equations of diffusion-convection using the difference schemes of second and fourth order approximation error. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 1, pp. 47-62. http://geodesic.mathdoc.fr/item/VYURV_2016_5_1_a4/