Geodesic
Analytical and numerical solutions of two-dimensional problems of heat conduction and electronic optics
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 4, pp. 345-352

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This work is devoted to a comparative analysis of the effectiveness of various methods for the numerical solution of a non-stationary two-dimensional problem of heat conduction in a cylindrical coordinate system in the absence of axial symmetry. The analysis is carried out on the basis of the obtained analytical solution of the two-dimensional problem of heat conduction in a steady state. The results of this work are of great applied importance in calculating the processes of gas transportation through offshore pipelines, as well as in calculating the electrostatic field of focusing systems during transportation of charged particle beams in problems of electronic optics.
Keywords: offshore gas pipelines, frontal interval method, heat exchange model, numerical method with increased accuracy, electronic optics. 
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     author = {G. I. Kurbatova and E. M. Vinogradova},
     title = {Analytical and numerical solutions of two-dimensional problems of heat conduction and electronic optics},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     volume = {17},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2021_17_4_a2/}
}
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G. I. Kurbatova; E. M. Vinogradova. Analytical and numerical solutions of two-dimensional problems of heat conduction and electronic optics. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 4, pp. 345-352. http://geodesic.mathdoc.fr/item/VSPUI_2021_17_4_a2/