Article · Mathematical Methods in the Applied Sciences · December 16, 2025

CMMSE: On the Problem With Impulse Effects for Nonlinear ODEs

Agila B. Tleulessova, Aidana S. Orazbekova

Abstract

ABSTRACT The article considers a boundary value problem for a system of nonlinear ordinary differential equations that includes impulse effects. Such a model plays an important role in describing processes in which abrupt changes occur at certain points in time. The study obtained sufficient conditions for the existence of isolated solutions to the specified boundary value problem, which ensures an adequate reflection of the behavior of impulse systems within the framework of the mathematical model. To find solutions, algorithms were proposed based on the parameterization method, which allows one to effectively take into account the discontinuities caused by impulses. A numerical implementation of these algorithms was also performed, which confirmed their applicability and efficiency in solving such problems. The obtained results can be useful in various applied areas, such as mechanics, electrical engineering and biology, where systems are often subject to sudden changes under the influence of external factors. In general, the work carried out contributes to the development of the theory and methods for solving nonlinear boundary value problems with impulse effects, opening up opportunities for further research and engineering applications.

Nonlinear Differential Equations AnalysisDifferential Equations and Boundary ProblemsAdvanced Differential Equations and Dynamical Systemsimpulsive differential equationsnonlinear ordinary differential equationsboundary value problems

CMMSE: On the Problem With Impulse Effects for Nonlinear ODEs

Abstract

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