Applications of Nonlinear Ordinary and Partial Differential Equations in the Real World
Pratibha Shrivastava
Research Scholar, Shri Krishna University, Chhatarpur, M.P., India
Dr Dileep Singh
Assistant Professor, Department of Mathematics, Shri Krishna University, Chhatarpur, M.P., India
Receiving Date:
2026-03-16
Acceptance Date:
2026-04-21
Publication Date:
2026-05-12
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http://doi.org/10.37648/ijrst.v16i02.008
Abstract
This paper presents a comprehensive analysis of the methods used to solve ordinary differential equations (ODEs), which may be better understood if they are first categorized. When classifying differential equations, the three main criteria are homogeneity, linearity, and order. Linearity is the property that a function and its derivatives exhibit, while order is the property that determines the position of a differential equation relative to the highest derivative. All terms in a homogeneous equation relate to the dependent variable or its derivatives; however, in a non-homogeneous equation there are also independent terms. Rather than being purely theoretical, these categories really dictate the solutions' characteristics and direct the selection of solution techniques. When it comes to mechanical vibrations and electrical circuits, for example, second-order equations are common, while first-order differential equations often depict straightforward growth or decay processes.
Keywords:
ODE applications; Euler's method; Runge-Kutta Methods; Ordinary Differential Equations (ODEs)
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