Quasilinearization method for an impulsive integro-differential system with delay.

Area of Science:

• Differential Equations
• Numerical Analysis
• Mathematical Modeling

Background:

• Impulsive integro-differential equations with delay present significant mathematical challenges.
• Existing methods for solving such systems often lack efficiency or broad applicability.
• Extremal solutions require specialized techniques for accurate determination.

Purpose of the Study:

• To develop and present a novel numerical method for analyzing impulsive integro-differential systems with delay.
• To establish uniform and quadratic convergence of solution sequences to extremal solutions.
• To broaden the applicability of existing analytical and numerical techniques in this field.

Main Methods:

• The study employs the method of quasilinearization.
• Monotone iterative techniques are utilized to construct solution sequences.
• Convergence analysis is performed to demonstrate the method's efficacy.

Main Results:

• The paper demonstrates uniform and quadratic convergence of solution sequences.
• The method successfully converges to extremal solutions of the considered systems.
• The obtained results offer greater generality and applicability compared to prior research.

Conclusions:

• The proposed method provides an efficient and reliable approach for solving impulsive integro-differential equations with delay.
• The findings significantly advance the understanding and computational treatment of these complex mathematical models.
• This work highlights the power of combining quasilinearization and monotone iterative techniques for such problems.