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Functional continuous Runge–Kutta methods with reuse. / Eremin, Alexey S.

в: Applied Numerical Mathematics, Том 146, 01.12.2019, стр. 165-181.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

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Eremin, AS 2019, 'Functional continuous Runge–Kutta methods with reuse', Applied Numerical Mathematics, Том. 146, стр. 165-181. https://doi.org/10.1016/j.apnum.2019.07.012

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Author

Eremin, Alexey S. / Functional continuous Runge–Kutta methods with reuse. в: Applied Numerical Mathematics. 2019 ; Том 146. стр. 165-181.

BibTeX

@article{b95571f4fa294e3b86003d831636db68,
title = "Functional continuous Runge–Kutta methods with reuse",
abstract = "In the paper explicit functional continuous Runge–Kutta and Runge–Kutta–Nystr{\"o}m methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the special form are constructed with the reuse of the last stage of the step. The order conditions for Runge–Kutta–Nystr{\"o}m methods are derived. Methods of orders three, four and five which require less computations than the known methods are presented. Numerical solution of the test problems confirm the convergence order of the new methods and their lower computational cost is performed.",
keywords = "Continuous Runge–Kutta, Delay differential equations, Functional differential equations, Overlapping, NUMERICAL-SOLUTION, Continuous Runge-Kutta",
author = "Eremin, {Alexey S.}",
year = "2019",
month = dec,
day = "1",
doi = "10.1016/j.apnum.2019.07.012",
language = "English",
volume = "146",
pages = "165--181",
journal = "Applied Numerical Mathematics",
issn = "0168-9274",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Functional continuous Runge–Kutta methods with reuse

AU - Eremin, Alexey S.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - In the paper explicit functional continuous Runge–Kutta and Runge–Kutta–Nyström methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the special form are constructed with the reuse of the last stage of the step. The order conditions for Runge–Kutta–Nyström methods are derived. Methods of orders three, four and five which require less computations than the known methods are presented. Numerical solution of the test problems confirm the convergence order of the new methods and their lower computational cost is performed.

AB - In the paper explicit functional continuous Runge–Kutta and Runge–Kutta–Nyström methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the special form are constructed with the reuse of the last stage of the step. The order conditions for Runge–Kutta–Nyström methods are derived. Methods of orders three, four and five which require less computations than the known methods are presented. Numerical solution of the test problems confirm the convergence order of the new methods and their lower computational cost is performed.

KW - Continuous Runge–Kutta

KW - Delay differential equations

KW - Functional differential equations

KW - Overlapping

KW - NUMERICAL-SOLUTION

KW - Continuous Runge-Kutta

UR - http://www.scopus.com/inward/record.url?scp=85068882589&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/functional-continuous-rungekutta-methods-reuse

U2 - 10.1016/j.apnum.2019.07.012

DO - 10.1016/j.apnum.2019.07.012

M3 - Article

AN - SCOPUS:85068882589

VL - 146

SP - 165

EP - 181

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -

ID: 43756490