Criteria of Solvability for Asymmetric Difference Schemes at High-Accuracy Approximation of Boundary Conditions

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Criteria of Solvability for Asymmetric Difference Schemes at High-Accuracy Approximation of Boundary Conditions. / Paasonen, V. I.

In: Numerical Analysis and Applications, Vol. 17, No. 3, 6, 09.2024, p. 276-286.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{e022d62a99614495884ab907eb911239,

title = "Criteria of Solvability for Asymmetric Difference Schemes at High-Accuracy Approximation of Boundary Conditions",

abstract = "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.",

keywords = "diagonal dominance, flux balance conditions, high-accuracy boundary conditions, multipoint derivative approximation",

author = "Paasonen, {V. I.}",

note = "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).",

year = "2024",

month = sep,

doi = "10.1134/S1995423924030066",

language = "English",

volume = "17",

pages = "276--286",

journal = "Numerical Analysis and Applications",

issn = "1995-4239",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "3",

}

RIS

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