Analytical Solution of Initial Value Problem for Ordinary Differential Equation with Singular Perturbation and Piecewise Constant Argument


Artykbayeva Z.N. Mirzakulova A.E. Assilkhan A.A.
30 June 2024al-Farabi Kazakh State National University

KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2024#122Issue 23 - 13 pp.

The study of differential equations with piecewise constant arguments has been treated widely in the literature. This type of equation, in which techniques of differential and difference equations are combined, models, among others, some biological phenomena, the stabilization of hybrid control systems with feedback discrete controller or damped oscillators.The first studies in this field have been given in 1984, after this, some papers related with stability, oscillation properties and existence of periodic outcomes have been treated by several authors.The manuscript is crafted as follows: Section 2 outlines the primary methodologies adopted throughout the inquiry.Section 3 is dedicated to obtaining the exclusive( outcome) to the issue. We formulate a series of difference y(θ equations overseeing the vectori) y, i = 1, p which portray the constituents of the (θi) outcome. This generalized approach allows for a broader understanding of how to tackle such differential equations across various scenarios. These equations now form a recognized branch of the field of differential equations, and they are frequently used in biological and economic models. Undoubtedly, their applications will continue to increase in the future.

EPCA , initial functions , initial value problem

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Al-Farabi Kazakh National University, Almaty, Kazakhstan

Al-Farabi Kazakh National University

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