Электронный каталог

Статья

Malykh, M.D.
Finite Difference Models of Dynamical Systems with Polynomial Right-Hand Side : [Abstract] / M.D.Malykh, E.A.Ayryan, I.T.Dulatov, L.O.Lapshenkova, L.A.Sevastianov // Физика элементарных частиц и атомного ядра. – 2025. – Т. 56, № 6 : Международная конференция «Математическое моделирование и вычислительная физика», Ереван, Армения, 21–25 октября 2024 г. : Материалы. – P. 1974-1975. – URL: https://www1.jinr.ru/Pepan/v-56-6/Malykh.pdf.

We provide a detailed examination of difference schemes that establish a one-toone correspondence between time layers, commonly known as Kahan’s scheme or reversible difference schemes. These mathematical frameworks play a crucial role in numerical analysis and computational mathematics, enabling accurate modeling of dynamic systems. We discuss the applications of these schemes, particularly in dynamic systems with quadratic right-hand sides, which are found in various fields such as physics, engineering, and applied mathematics. These systems often describe complex phenomena, including mechanical vibrations and fluid dynamics. Additionally, we explore the integration of Kahan’s scheme with the direct method for solving partial differential equations in mathematical physics. This combination aims to enhance the accuracy and computational efficiency of numerical solutions. By investigating the correlation between these methodologies, we seek to advance numerical techniques for addressing complex dynamic systems. The findings indicate that this integration improves the stability and convergence of solutions, highlighting the potential of Kahan’s scheme and reversible difference schemes in tackling challenges across diverse scientific disciplines



Спец.(статьи,препринты) = С 17 а - Численный анализ. Исчисление конечных разностей. Интерполирование
Спец.(статьи,препринты) = С 17 д - Численное решение дифференциальных и интегральных уравнений. Разностные методы
ОИЯИ = ОИЯИ (JINR)2025