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Criteria of Solvability for Asymmetric Difference Schemes at High-Accuracy Approximation of Boundary Conditions. / Paasonen, V. I.
в: Numerical Analysis and Applications, Том 17, № 3, 6, 09.2024, стр. 276-286.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Criteria of Solvability for Asymmetric Difference Schemes at High-Accuracy Approximation of Boundary Conditions
AU - Paasonen, V. I.
N1 - The results presented in Sections 1-3 were obtained under State Assignment of the Ministry of Education and Science for FRC ICT; the results presented in Sections 4 and 5 were obtained with support of the Russian Science Foundation (project no. 20-11-20040).
PY - 2024/9
Y1 - 2024/9
N2 - In this paper we study a technology of calculating difference problems with internal boundary conditions of flux balance constructed by means of one-sided multipoint difference analogs of first derivatives of arbitrary order of accuracy. The technology is suitable for any type of differential equations to be solved and admits the same type of realization at any order of accuracy. In contrast to the approximations based on an extended system of equations, this technology does not lead to complications in splitting multidimensional problems into one-dimensional ones. Sufficient conditions of solvability and stability are formulated for realizations of the algorithms by using the double-sweep method for boundary conditions of arbitrary order of accuracy. Their proof is based on a reduction of the multipoint boundary conditions to a form that does not violate the tridiagonal structure of the matrices and the establishment of conditions of diagonal dominance in the transformed matrix rows corresponding to the external and internal boundary conditions.
AB - In this paper we study a technology of calculating difference problems with internal boundary conditions of flux balance constructed by means of one-sided multipoint difference analogs of first derivatives of arbitrary order of accuracy. The technology is suitable for any type of differential equations to be solved and admits the same type of realization at any order of accuracy. In contrast to the approximations based on an extended system of equations, this technology does not lead to complications in splitting multidimensional problems into one-dimensional ones. Sufficient conditions of solvability and stability are formulated for realizations of the algorithms by using the double-sweep method for boundary conditions of arbitrary order of accuracy. Their proof is based on a reduction of the multipoint boundary conditions to a form that does not violate the tridiagonal structure of the matrices and the establishment of conditions of diagonal dominance in the transformed matrix rows corresponding to the external and internal boundary conditions.
KW - diagonal dominance
KW - flux balance conditions
KW - high-accuracy boundary conditions
KW - multipoint derivative approximation
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85203859563&origin=inward&txGid=65572b1853b3b13e7ac93c7a38cae420
UR - https://elibrary.ru/item.asp?id=69201027
UR - https://www.mendeley.com/catalogue/b332eae3-69a8-323f-80c0-413d2af4c29a/
U2 - 10.1134/S1995423924030066
DO - 10.1134/S1995423924030066
M3 - Article
VL - 17
SP - 276
EP - 286
JO - Numerical Analysis and Applications
JF - Numerical Analysis and Applications
SN - 1995-4239
IS - 3
M1 - 6
ER -
ID: 60724487