Some issues with the numerical treatment of delay differential equations

Standard

Some issues with the numerical treatment of delay differential equations. / Eremin, A. S.; Humphries, A. R.; Lobaskin, A. A.

International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. ed. / Theodore E. Simos; Charalambos Tsitouras. American Institute of Physics, 2020. 100003 (AIP Conference Proceedings; Vol. 2293).

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

Harvard

Eremin, AS, Humphries, AR & Lobaskin, AA 2020, Some issues with the numerical treatment of delay differential equations. in TE Simos & C Tsitouras (eds), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019., 100003, 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/10.1063/5.0027149

APA

Eremin, A. S., Humphries, A. R., & Lobaskin, A. A. (2020). Some issues with the numerical treatment of delay differential equations. In T. E. Simos, & C. Tsitouras (Eds.), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019 [100003] (AIP Conference Proceedings; Vol. 2293). American Institute of Physics. https://doi.org/10.1063/5.0027149

Vancouver

Eremin AS, Humphries AR, Lobaskin AA. Some issues with the numerical treatment of delay differential equations. In Simos TE, Tsitouras C, editors, International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. American Institute of Physics. 2020. 100003. (AIP Conference Proceedings). https://doi.org/10.1063/5.0027149

Author

Eremin, A. S. ; Humphries, A. R. ; Lobaskin, A. A. / Some issues with the numerical treatment of delay differential equations. International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. editor / Theodore E. Simos ; Charalambos Tsitouras. American Institute of Physics, 2020. (AIP Conference Proceedings).

BibTeX

@inproceedings{6646ecf2913841b98ed716d2a4c380a2,

title = "Some issues with the numerical treatment of delay differential equations",

abstract = "In this paper several problems arising when implementing methods to numerically solve delay-differential equations, such as overlapping, difficulties with error estimation, discontinuities of solution derivatives and the detection of such discontinuity points, are considered. Several approaches to each issue are discussed. The best solutions for explicit and diagonally implicit Runge-Kutta methods for DDEs are reported. A numerical comparison between a method implementing the handling of such problems, and the Matlab code ddesd, demonstrates that our method is more efficient.",

author = "Eremin, {A. S.} and Humphries, {A. R.} and Lobaskin, {A. A.}",

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 = "10.1063/5.0027149",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

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

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

address = "United States",

}

RIS

TY - GEN

T1 - Some issues with the numerical treatment of delay differential equations

AU - Eremin, A. S.

AU - Humphries, A. R.

AU - Lobaskin, A. A.

PY - 2020/11/24

Y1 - 2020/11/24

N2 - In this paper several problems arising when implementing methods to numerically solve delay-differential equations, such as overlapping, difficulties with error estimation, discontinuities of solution derivatives and the detection of such discontinuity points, are considered. Several approaches to each issue are discussed. The best solutions for explicit and diagonally implicit Runge-Kutta methods for DDEs are reported. A numerical comparison between a method implementing the handling of such problems, and the Matlab code ddesd, demonstrates that our method is more efficient.

AB - In this paper several problems arising when implementing methods to numerically solve delay-differential equations, such as overlapping, difficulties with error estimation, discontinuities of solution derivatives and the detection of such discontinuity points, are considered. Several approaches to each issue are discussed. The best solutions for explicit and diagonally implicit Runge-Kutta methods for DDEs are reported. A numerical comparison between a method implementing the handling of such problems, and the Matlab code ddesd, demonstrates that our method is more efficient.

UR - http://www.scopus.com/inward/record.url?scp=85098005705&partnerID=8YFLogxK

U2 - 10.1063/5.0027149

DO - 10.1063/5.0027149

M3 - Conference contribution

AN - SCOPUS:85098005705

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: 75468157