Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
Fourth-Order Method for Differential Equations with Discrete and Distributed Delays. / Eremin, Alexey S. ; Lobaskin, Aleksandr A. .
SCP 2020: Stability and Control Processes: International Conference Dedicated to the Memory of Professor Vladimir Zubov. Cham : Springer Nature, 2022. стр. 199-206 (Lecture Notes in Control and Information Sciences - Proceedings).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - Fourth-Order Method for Differential Equations with Discrete and Distributed Delays
AU - Eremin, Alexey S.
AU - Lobaskin, Aleksandr A.
N1 - Conference code: 4
PY - 2022/3/16
Y1 - 2022/3/16
N2 - Differential equations with discrete and distributed delays are considered. Explicit continuous-stage Runge–Kutta methods for state-dependent discrete delays based on functional continuous methods for retarded functional differential equations and Runge–Kutta methods for integro-differential equations based on methods for Volterra equations are combined to get a method suitable for both types of delays converging with order four. A method that requires six right-hand side evaluations and only two of its integral argument evaluations is presented. The questions of the practical implementation for delay differential equations within general non-smooth solutions are discussed. The numerical solution of test problems confirms the declared fourth order of convergence of the constructed method.
AB - Differential equations with discrete and distributed delays are considered. Explicit continuous-stage Runge–Kutta methods for state-dependent discrete delays based on functional continuous methods for retarded functional differential equations and Runge–Kutta methods for integro-differential equations based on methods for Volterra equations are combined to get a method suitable for both types of delays converging with order four. A method that requires six right-hand side evaluations and only two of its integral argument evaluations is presented. The questions of the practical implementation for delay differential equations within general non-smooth solutions are discussed. The numerical solution of test problems confirms the declared fourth order of convergence of the constructed method.
UR - https://proxy.library.spbu.ru:2096/chapter/10.1007/978-3-030-87966-2_21
UR - https://www.mendeley.com/catalogue/bb6b23c3-60bb-3e7e-ae09-e650de32c807/
U2 - https://doi.org/10.1007/978-3-030-87966-2_21
DO - https://doi.org/10.1007/978-3-030-87966-2_21
M3 - Conference contribution
SN - 978-3-030-87965-5
T3 - Lecture Notes in Control and Information Sciences - Proceedings
SP - 199
EP - 206
BT - SCP 2020: Stability and Control Processes
PB - Springer Nature
CY - Cham
T2 - Stability and Control Processes: International Conference Dedicated to the Memory of Professor Vladimir Zubov
Y2 - 5 October 2020 through 9 October 2020
ER -
ID: 94358167