Possible solutions of a linear homogeneous system of differential equations

Standard

Possible solutions of a linear homogeneous system of differential equations. / Kadry, S.; Alferov, G.; Ivanov, G.; Korolev, V.

International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. ed. / Theodore E. Simos; Theodore E. Simos; Theodore E. Simos; Theodore E. Simos; Theodore E. Simos; Charalambos Tsitouras. American Institute of Physics, 2020. 060002 (AIP Conference Proceedings; Vol. 2293).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Harvard

Kadry, S, Alferov, G , Ivanov, G & Korolev, V 2020, Possible solutions of a linear homogeneous system of differential equations. in TE Simos, TE Simos, TE Simos, TE Simos, TE Simos & C Tsitouras (eds), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019., 060002, AIP Conference Proceedings, vol. 2293, American Institute of Physics, International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019, Rhodes, Greece, 23/09/19. https://doi.org/10.1063/5.0026490

APA

Kadry, S., Alferov, G., Ivanov, G., & Korolev, V. (2020). Possible solutions of a linear homogeneous system of differential equations. In T. E. Simos, T. E. Simos, T. E. Simos, T. E. Simos, T. E. Simos, & C. Tsitouras (Eds.), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019 [060002] (AIP Conference Proceedings; Vol. 2293). American Institute of Physics. https://doi.org/10.1063/5.0026490

Vancouver

Kadry S, Alferov G , Ivanov G , Korolev V. Possible solutions of a linear homogeneous system of differential equations. In Simos TE, Simos TE, Simos TE, Simos TE, Simos TE, Tsitouras C, editors, International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. American Institute of Physics. 2020. 060002. (AIP Conference Proceedings). https://doi.org/10.1063/5.0026490

Author

Kadry, S. ; Alferov, G. ; Ivanov, G. ; Korolev, V. / Possible solutions of a linear homogeneous system of differential equations. International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. editor / Theodore E. Simos ; Theodore E. Simos ; Theodore E. Simos ; Theodore E. Simos ; Theodore E. Simos ; Charalambos Tsitouras. American Institute of Physics, 2020. (AIP Conference Proceedings).

BibTeX

@inproceedings{1bd5e65a7fb4484593ab195e7aa85394,

title = "Possible solutions of a linear homogeneous system of differential equations",

abstract = "In the present paper it is shown that the fundamental zero-normalized solution of a system of linear homogeneous differential equations can be represented as a formal series of products of exponential matrices. If the system satisfies the conditions of the Perron theorem on the triangulation of a system of equations, then the solution of such a system can be represented as a finite product of exponential matrices. In addition, a formula for differentiating an exponential matrix function is derived, and the problem of constructing a transformation that reduces a system of homogeneous differential equations to a triangular form is considered.",

keywords = "Exponential matrices, Linear homogeneous differential equations, Schmidt orthogonalization method",

author = "S. Kadry and G. Alferov and G. Ivanov and V. Korolev",

note = "Publisher Copyright: {\textcopyright} 2020 American Institute of Physics Inc.. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 ; Conference date: 23-09-2019 Through 28-09-2019",

year = "2020",

month = nov,

day = "24",

doi = "10.1063/5.0026490",

language = "English",

isbn = "9780735440258",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

editor = "Simos, {Theodore E.} and Simos, {Theodore E.} and Simos, {Theodore E.} and Simos, {Theodore E.} and Simos, {Theodore E.} and Charalambos Tsitouras",

booktitle = "International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019",

address = "United States",

}

RIS

TY - GEN

T1 - Possible solutions of a linear homogeneous system of differential equations

AU - Kadry, S.

AU - Alferov, G.

AU - Ivanov, G.

AU - Korolev, V.

PY - 2020/11/24

Y1 - 2020/11/24

N2 - In the present paper it is shown that the fundamental zero-normalized solution of a system of linear homogeneous differential equations can be represented as a formal series of products of exponential matrices. If the system satisfies the conditions of the Perron theorem on the triangulation of a system of equations, then the solution of such a system can be represented as a finite product of exponential matrices. In addition, a formula for differentiating an exponential matrix function is derived, and the problem of constructing a transformation that reduces a system of homogeneous differential equations to a triangular form is considered.

AB - In the present paper it is shown that the fundamental zero-normalized solution of a system of linear homogeneous differential equations can be represented as a formal series of products of exponential matrices. If the system satisfies the conditions of the Perron theorem on the triangulation of a system of equations, then the solution of such a system can be represented as a finite product of exponential matrices. In addition, a formula for differentiating an exponential matrix function is derived, and the problem of constructing a transformation that reduces a system of homogeneous differential equations to a triangular form is considered.

KW - Exponential matrices

KW - Linear homogeneous differential equations

KW - Schmidt orthogonalization method

UR - http://www.scopus.com/inward/record.url?scp=85098001974&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/5a49f05e-6f2b-3073-8c97-a8ace59138ff/

U2 - 10.1063/5.0026490

DO - 10.1063/5.0026490

M3 - Conference contribution

AN - SCOPUS:85098001974

SN - 9780735440258

T3 - AIP Conference Proceedings

BT - International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019

A2 - Simos, Theodore E.

A2 - Tsitouras, Charalambos

PB - American Institute of Physics

T2 - International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019

Y2 - 23 September 2019 through 28 September 2019

ER -

ID: 72144265