Advanced Numerical Methods for Solving Nonlinear Differential Equations: Theory, Algorithms, and Applications

Abstract

Nonlinear differential equations (NDEs) are considered a crucial part in modeling complex physical, biological, and engineering systems. Classical numerical methods exhibit limitations in stability, accuracy, and efficiency. The purpose of this paper is to present a comprehensive review and analysis of advanced methods for solving NDEs. In this paper, we focused on recent numerical novel algorithms and laid the theoretical foundations and practical performance considerations.