Functional continuous Runge-Kutta-Nystrom methods

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Functional continuous Runge-Kutta-Nystrom methods. / Eremin, Alexey S.

In: Electronic Journal of Qualitative Theory of Differential Equations, No. 11, 2016, p. 1-17.

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

Author

Eremin, Alexey S. / Functional continuous Runge-Kutta-Nystrom methods. In: Electronic Journal of Qualitative Theory of Differential Equations. 2016 ; No. 11. pp. 1-17.

BibTeX

@article{6d3371fe23c04f80abd9ff99cf49d9d2,

title = "Functional continuous Runge-Kutta-Nystrom methods",

abstract = "Numerical methods for solving retarded functional differential equations of the second order with right-hand side independent of the function derivative are considered. The approach used by E. Nystrom for second-order ordinary differential equations with the mentioned property is applied for construction of effective functional continuous methods. Order conditions are formulated, and example methods are constructed. They have fewer stages than Runge-Kutta type methods of the same order. Application of the constructed methods to test problems confirms their declared orders of convergence.",

keywords = "delay differential equations, second order equations, Runge-Kutta methods, functional continuous methods, DIFFERENTIAL EQUATIONS, NUMERICAL-SOLUTION",

author = "Eremin, {Alexey S.}",

year = "2016",

doi = "10.14232/ejqtde.2016.8.11",

language = "Английский",

pages = "1--17",

journal = "Electronic Journal of Qualitative Theory of Differential Equations",

issn = "1417-3875",

publisher = "University of Szeged",

number = "11",

note = "null ; Conference date: 01-07-2015 Through 04-07-2015",

}

RIS

TY - JOUR

T1 - Functional continuous Runge-Kutta-Nystrom methods

AU - Eremin, Alexey S.

PY - 2016

Y1 - 2016

N2 - Numerical methods for solving retarded functional differential equations of the second order with right-hand side independent of the function derivative are considered. The approach used by E. Nystrom for second-order ordinary differential equations with the mentioned property is applied for construction of effective functional continuous methods. Order conditions are formulated, and example methods are constructed. They have fewer stages than Runge-Kutta type methods of the same order. Application of the constructed methods to test problems confirms their declared orders of convergence.

AB - Numerical methods for solving retarded functional differential equations of the second order with right-hand side independent of the function derivative are considered. The approach used by E. Nystrom for second-order ordinary differential equations with the mentioned property is applied for construction of effective functional continuous methods. Order conditions are formulated, and example methods are constructed. They have fewer stages than Runge-Kutta type methods of the same order. Application of the constructed methods to test problems confirms their declared orders of convergence.

KW - delay differential equations

KW - second order equations

KW - Runge-Kutta methods

KW - functional continuous methods

KW - DIFFERENTIAL EQUATIONS

KW - NUMERICAL-SOLUTION

U2 - 10.14232/ejqtde.2016.8.11

DO - 10.14232/ejqtde.2016.8.11

M3 - статья

SP - 1

EP - 17

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

SN - 1417-3875

IS - 11

Y2 - 1 July 2015 through 4 July 2015

ER -

ID: 7579993