Academic Journal
EXPLICIT FIFTH-ORDER HYBRID METHODS FOR DYNAMICAL SYSTEMS WITH DELAY ; ЯВНІ ГІБРИДНІ МЕТОДИ П’ЯТОГО ПОРЯДКУ ЗБІЖНОСТІ ДЛЯ ДИНАМІЧНИХ СИСТЕМ З ЗАПІЗНЮВАННЯМ
| العنوان: | EXPLICIT FIFTH-ORDER HYBRID METHODS FOR DYNAMICAL SYSTEMS WITH DELAY ; ЯВНІ ГІБРИДНІ МЕТОДИ П’ЯТОГО ПОРЯДКУ ЗБІЖНОСТІ ДЛЯ ДИНАМІЧНИХ СИСТЕМ З ЗАПІЗНЮВАННЯМ |
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| المؤلفون: | Печук, Василій, Бондаренко , Наталія |
| المصدر: | APPLIED GEOMETRY AND ENGINEERING GRAPHICS; No. 101 (2021); 168-180 ; Прикладна геометрія та інженерна графіка; № 101 (2021); 168-180 ; 0131-579X ; 10.32347/0131-579x.2021.101 |
| بيانات النشر: | Kyiv National University of Construction and Architecture |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | системи диференціальних рівнянь з запізнюванням, чисельні методи, методи Рунге-Кутти, поліноми Ньютона, екстраполяція, Time-delay systems of differential equations, numerical methods, Runge-Kutta methods, Newton polynomials, Taylor formula, extrapolation |
| الوصف: | In the paper we consider the systems of delay differential equations, which are mathematical models of many technical processes with delay in time. An explicit fifth-order hybrid method for systems of delay differential equations for the variable step of numerical integration is constructed. This algorithm is based on the most commonly used explicit fifth-order Runge-Kutta methods for ordinary systems of differential equations and the construction of Newton polynomials for the prehistory of the model and Taylor formula. The basic principles of construction of such explicit hybrid methods of higher orders of convergence are given. An accurate estimate of the local error of numerical integration by this method is obtained. This algorithm allows the use of numerical integration steps greater than the magnitude of the delay or procedures for adjusting the magnitude of the step depending on the calculation error. Such a problem of numerical integration of time-delay dynamical systems occurs when the time interval is large enough compared to the delay. Implicit continuous Runge-Kutta methods were previously used for numerical integration such problems, which complicated the numerical algorithm, because nonlinear systems of equations have to be solved at each step of numerical integration. The explicit hybrid method constructed by us for systems of delay differential equations is convenient for programming, has a high speed of calculation of numerical solution, in comparison with implicit methods for such models of problems. Also, this method has no restrictions on the magnitude of the delay, in contrast to the hybrid methods with decomposition in Taylor series for delay. The method obtained by us can be used to construct maps of dynamic modes in the study of regular and chaotic behavior of time-delay dynamical systems. ; У роботі розглядаються системи диференціальних рівнянь з запізнюванням, які є математичними моделями багатьох технічних процесів з запізнюванням у часі. Побудовано явний гібридний метод п’ятого ... |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | application/pdf |
| اللغة: | Ukrainian |
| Relation: | http://ageg.knuba.edu.ua/article/view/256332/253571; http://ageg.knuba.edu.ua/article/view/256332 |
| DOI: | 10.32347/0131-579X.2021.101.168-180 |
| الاتاحة: | http://ageg.knuba.edu.ua/article/view/256332 https://doi.org/10.32347/0131-579X.2021.101.168-180 |
| Rights: | Авторське право (c) 2021 Печук Василь, Бондаренко Наталія ; http://creativecommons.org/licenses/by/4.0 |
| رقم الانضمام: | edsbas.E1EBF9E |
| قاعدة البيانات: | BASE |
| DOI: | 10.32347/0131-579X.2021.101.168-180 |
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