International Journal For Multidisciplinary Research

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Numerical Methods for Solving Impulsive Differential Equations: Challenges, Methods, and Innovations

Author(s) Venkatachalapathi Uday, Dr. Gautam Kumar Rajput
Country India
Abstract Impulsive differential equations (IDEs) are a class of differential equations that model dynamic systems subject to sudden changes at distinct moments in time, called impulses. These equations arise in a variety of fields such as physics, biology, economics, and engineering, often-representing phenomena where processes experience discontinuities, such as shock waves, sudden force applications, or rapid switching. The study of numerical methods for solving IDEs is crucial for their practical applications, as analytical solutions are rarely available due to the non-smooth nature of impulses. This paper discusses the challenges in solving IDEs numerically, the methods developed to tackle these challenges, and recent innovations that have improved the accuracy and efficiency of numerical simulations.
Keywords : Impulsive differential equations, numerical methods, discontinuities, Runge-Kutta methods, adaptive methods, hybrid methods, impulse correction, machine learning, computational complexity.
Field Mathematics
Published In Volume 6, Issue 6, November-December 2024
Published On 2024-11-13
Cite This Numerical Methods for Solving Impulsive Differential Equations: Challenges, Methods, and Innovations - Venkatachalapathi Uday, Dr. Gautam Kumar Rajput - IJFMR Volume 6, Issue 6, November-December 2024. DOI 10.36948/ijfmr.2024.v06i06.30538
DOI https://doi.org/10.36948/ijfmr.2024.v06i06.30538
Short DOI https://doi.org/g8rd33
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