Geodesic
Two variants of economical method for solving of the transport equation in $r-z$ geometry on the basis of transition to Vladimirov's variables
Matematičeskoe modelirovanie, Tome 18 (2006) no. 7, pp. 43-52

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The method for numerical solving of 2D steady transport equation on the basis of transition to the Vladimirov's variables have been suggested. The spatial and angular meshes are rigidly connected in classical variant of Vladimirov's method, that is not convenient in many practical cases. The algorithm for equation solving is suggested with independent construction of these meshes. It allows explicitly resolve the structure of all logarithmical discontinuities of solution, which is immanent for problems with spherical and cylindrical geometry. Two variants of the method has been suggested: pure characteristical one and conservative characteristical method. It has been shown for test problem with exact solution that for rough meshes conservative characteristical method allows to construct solution of high accuracy, especially for quasi-diffusion tensor. 
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     author = {E. N. Aristova and D. F. Baydin and V. Ya. Gol'din},
     title = {Two variants of economical method for solving of the transport equation in $r-z$ geometry on the basis of transition to {Vladimirov's} variables},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {43--52},
     publisher = {mathdoc},
     volume = {18},
     number = {7},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_7_a2/}
}
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E. N. Aristova; D. F. Baydin; V. Ya. Gol'din. Two variants of economical method for solving of the transport equation in $r-z$ geometry on the basis of transition to Vladimirov's variables. Matematičeskoe modelirovanie, Tome 18 (2006) no. 7, pp. 43-52. http://geodesic.mathdoc.fr/item/MM_2006_18_7_a2/