A highly accurate and efficient method for studying the dynamics of derivatives of different orders of a singularly perturbed equation
https://doi.org/10.22405/2226-8383-2025-26-4-357-369
Abstract
The purpose of this article is to construct a highly accurate and efficient numerical method for studying the dynamics of derivatives of various orders of a singularly perfected differential
equation. In the method of preliminary integration of the highest derivative, the equations and the right part are represented as finite series according to Chebyshev polynomials of the first
kind with unknown expansion coefficients. Before solving the problem, the selected series is pre-integrated and expressions are found in the form of series for all lower derivatives and the
desired solution. Unknown constants appearing during series integration are determined from additional conditions of the problem. Unknown coefficients are determined from a system of
algebraic equations and putting them in the right series, the derivatives and the solution of the problem are calculated.
About the Authors
Chori Begalievich Normurodov
Termez State University
Uzbekistan
Uzbekistan
Nasiba Turakhanovna Djuraeva
Termez State University
Uzbekistan
Uzbekistan
Mohira Majidovna Normatova
Termez State University
Uzbekistan
Uzbekistan
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Review
For citations:
Normurodov Ch.B., Djuraeva N.T., Normatova M.M. A highly accurate and efficient method for studying the dynamics of derivatives of different orders of a singularly perturbed equation. Chebyshevskii Sbornik. 2025;26(4):357-369. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-357-369
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