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Efficient accurate non-iterative breaking point detection and computation for state-dependent delay differential equations. / Eremin, A.; Humphries, A. R.

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). Springer Nature, 2015.

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

Harvard

Eremin, A & Humphries, AR 2015, Efficient accurate non-iterative breaking point detection and computation for state-dependent delay differential equations. in PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). Springer Nature. https://doi.org/10.1063/1.4912436

APA

Eremin, A., & Humphries, A. R. (2015). Efficient accurate non-iterative breaking point detection and computation for state-dependent delay differential equations. In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014) Springer Nature. https://doi.org/10.1063/1.4912436

Vancouver

Eremin A, Humphries AR. Efficient accurate non-iterative breaking point detection and computation for state-dependent delay differential equations. In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). Springer Nature. 2015 https://doi.org/10.1063/1.4912436

Author

Eremin, A. ; Humphries, A. R. / Efficient accurate non-iterative breaking point detection and computation for state-dependent delay differential equations. PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). Springer Nature, 2015.

BibTeX

@inproceedings{9a7d22bd8c054007a0439d156249afd2,
title = "Efficient accurate non-iterative breaking point detection and computation for state-dependent delay differential equations",
abstract = "When solving delay differential equations (DDEs) with state-dependent delays the problem of breaking point detection is important. Points where the solution is not smooth enough to provide the order of the method must be included into the computational mesh, otherwise a reduction in the order of the solution will result. The problem, however is to detect and compute such points efficiently. Breaking points arise every time a delay falls on a previous breaking point (either of the calculated solution or in the history function). In the case of retarded DDEs the new breaking point is (at least) one order smoother than the previous breaking point that gave rise to it. For fixed or time-dependent delays the breaking points can be precomputed independent of the solution, but for state-dependent delays the positions of the breaking points depend on the computed solution. If a breaking point is detected and the step-size is changed in order to incorporate the point into the mesh, then the new step-size generates a n",
author = "A. Eremin and Humphries, {A. R.}",
year = "2015",
doi = "10.1063/1.4912436",
language = "English",
isbn = "9780735412873",
booktitle = "PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014)",
publisher = "Springer Nature",
address = "Germany",

}

RIS

TY - GEN

T1 - Efficient accurate non-iterative breaking point detection and computation for state-dependent delay differential equations

AU - Eremin, A.

AU - Humphries, A. R.

PY - 2015

Y1 - 2015

N2 - When solving delay differential equations (DDEs) with state-dependent delays the problem of breaking point detection is important. Points where the solution is not smooth enough to provide the order of the method must be included into the computational mesh, otherwise a reduction in the order of the solution will result. The problem, however is to detect and compute such points efficiently. Breaking points arise every time a delay falls on a previous breaking point (either of the calculated solution or in the history function). In the case of retarded DDEs the new breaking point is (at least) one order smoother than the previous breaking point that gave rise to it. For fixed or time-dependent delays the breaking points can be precomputed independent of the solution, but for state-dependent delays the positions of the breaking points depend on the computed solution. If a breaking point is detected and the step-size is changed in order to incorporate the point into the mesh, then the new step-size generates a n

AB - When solving delay differential equations (DDEs) with state-dependent delays the problem of breaking point detection is important. Points where the solution is not smooth enough to provide the order of the method must be included into the computational mesh, otherwise a reduction in the order of the solution will result. The problem, however is to detect and compute such points efficiently. Breaking points arise every time a delay falls on a previous breaking point (either of the calculated solution or in the history function). In the case of retarded DDEs the new breaking point is (at least) one order smoother than the previous breaking point that gave rise to it. For fixed or time-dependent delays the breaking points can be precomputed independent of the solution, but for state-dependent delays the positions of the breaking points depend on the computed solution. If a breaking point is detected and the step-size is changed in order to incorporate the point into the mesh, then the new step-size generates a n

U2 - 10.1063/1.4912436

DO - 10.1063/1.4912436

M3 - Conference contribution

SN - 9780735412873

BT - PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014)

PB - Springer Nature

ER -

ID: 3928087