Advancements and Applications of Numerical Methods in Engineering and Scientific

Abstract

Numerical methods form the core of modern computational science, providing efficient techniques for solving mathematical problems that lack closed-form analytical solutions. This paper explores the development, implementation, and application of key numerical methods including root-finding algorithms, numerical integration, finite difference methods, and iterative solutions of linear and nonlinear systems. Emphasis is placed on their significance in solving differential equations, optimization problems, and real-time simulations in engineering and physical sciences. The paper also discusses error analysis, convergence criteria, and stability aspects that govern the accuracy and reliability of numerical techniques. Through case studies in fluid mechanics, heat transfer, and structural analysis, the utility and adaptability of these methods are demonstrated. This study aims to offer researchers and engineers a comprehensive understanding of how numerical methods enhance problem-solving capabilities across diverse domains.

Cite as:

Awasare Anant, & P. Thorat. (2025). Advancements and Applications of Numerical Methods in Engineering and Scientific Research. Journal of Applied Mathematics and Statistical Analysis, 6(2), 20–26. 

https://doi.org/10.5281/zenodo.16411388