EVALUATING PERFORMANCE: CONVERGENCE ORDER, CONSISTENCY, AND STABILITY IN RECENTLY PROPOSED SCHEMES

Abstract

Mathematical modeling serves as a vital tool for interpreting real-world scenarios through the lens of mathematical symbols and relationships, commonly applied across various disciplines including Sciences and Engineering. Through the development of models, researchers aim to gain insights into complex physical phenomena, often resulting in the formulation of differential equations containing derivatives of unknown functions. These equations, termed as Differential Equations, serve as foundational components in understanding phenomena spanning from physical sciences to fields as diverse as Economics, Medicine, Psychology, and Operation Research, extending even into domains like Biology and Anthropology. However, the quest for analytical solutions to these differential equations, stemming from real-life modeling endeavors, often presents formidable challenges. Many equations arising from such modeling efforts defy straightforward analytical solutions, necessitating the exploration of alternative methods for their resolution.

This abstract underscores the ubiquity of differential equations across numerous disciplines and emphasizes the significance of mathematical modeling in advancing understanding and problem-solving capabilities. It highlights the interdisciplinary nature of differential equations, transcending traditional boundaries and finding applications in diverse fields. Moreover, it acknowledges the inherent complexity associated with obtaining analytical solutions to these equations, paving the way for the exploration of alternative solution strategies.