Analytical and Numerical Investigation of Nonlinear Differential Equations: A Comprehensive Study
Keywords:
Nonlinear differential equations, analytical methods,numerical methods, perturbation techniques, bifurcation condition.Abstract
This paper explores nonlinear differential equations, focusing on their analytical properties,solution methods, and applications. We investigate specific examples of nonlinear ordinary and partial differential equations (ODEs/PDEs), highlighting recent developments in solution techniques, including perturbation methods, numerical schemes, and qualitative analysis. Applications in various physical and
biological systems are discussed to emphasize their significance in modeling complex phenomena.The analytical characteristics, solutions, and applications of nonlinear differential equations are the main topics of this paper. In order to highlight recent advancements in solution strategies, such as perturbation methods, numerical schemes, and qualitative analysis, we examine particular instances of nonlinear ordinary and partial differential equations (ODEs/PDEs). In order to highlight their importance in simulating complex processes, applications in a variety of physical and biological systems are examined.
References
Arnold, V. I. (2012). Geometrical methods in the theory of ordinary differential equations (Vol. 250). Springer Science & Business Media.
Orszag, S., & Bender, C. M. (1978). Advanced mathematical methods for scientists and engineers (pp. xiv+-593). New York: McGraw-Hill.
Boyce, W. E., &DiPrima, R. C. (2017). Elementary Differential Equations and Boundary Value Problems (11th ed.). Wiley.
