Author : Rajiv Thakur
Abstract : The complexity of nonlinear differential equations often necessitates the use of advanced numerical methods for their solution, particularly in engineering contexts where exact solutions are not feasible. This paper explores various advanced numerical techniques, such as the Runge-Kutta methods, finite difference methods, and the shooting method, which are applied to a range of nonlinear differential equations. The study emphasizes the efficiency and accuracy of these methods through several engineering case studies, including fluid dynamics, heat transfer, and structural analysis. Comparative analyses demonstrate the strengths and limitations of each method, providing guidance for selecting appropriate techniques for specific engineering applications. Additionally, the convergence, stability, and computational cost of each method are evaluated to offer a comprehensive understanding of their practical implementation.
Keywords : Nonlinear Differential Equations, Runge-Kutta Methods, Finite Difference Methods, Numerical Analysis, Engineering Applications
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