Ryan Nadar,
Shirish Kulkarni,
- Research,, DY Patil University, Charholi Budruk, Pune,, Maharashtra,, India.
- Assistant Professor,, DY Patil University, Charholi Budruk, Pune,, Maharashtra, India
Abstract
This research paper explores the fundamental role of various mathematical concepts in engineering and scientific fields like aerospace engineering, materials science, software development, and the energy sector. We delve into the applications of solving algebraic and transcendental equations, finite difference interpolation, numerical methods, solutions to ordinary differential equations (ODEs), and numerical solutions to partial differential equations (PDEs). By examining their applications in these diverse fields, we illustrate the critical importance of mathematics in driving innovation and technological advancements. Many applications in science and engineering depend on numerical techniques for solving differential equations. In situations where obtaining analytical solutions is challenging or impossible, these techniques allow for the approximation of solutions. Ordinary differential equations (ODEs) and partial differential equations (PDEs) are the two main categories of differential equations that are covered in this article. We will investigate their numerical solutions, going over methods such as Euler’s method, Runge-Katta methods for ODEs, and methods for PDEs such as Finite Difference and Finite Element. An indispensable tool in contemporary research and engineering is the numerical solution of ODEs and PDEs. Euler’s method, Runge-Kotta methods for ODEs, and FDM, FEM, and FVM for PDEs are examples of techniques that can solve difficult problems when analytical approaches are insufficient. The type of equation, the necessary accuracy, and the available processing resources all influence the approach choice. These numerical techniques are still developing and are providing increasingly accurate and effective answers to practical issues.
Keywords: Applications of Algebraic Equations, Interpolation, Numerical Methods, and Differential Equations, application in real life
[This article belongs to Journal of Aerospace Engineering & Technology (joaet)]
Ryan Nadar, Shirish Kulkarni. Numerical Solution of Ordinary Differential Equation and Solution of Partial Differential Equation. Journal of Aerospace Engineering & Technology. 2024; 14(03):1-10.
Ryan Nadar, Shirish Kulkarni. Numerical Solution of Ordinary Differential Equation and Solution of Partial Differential Equation. Journal of Aerospace Engineering & Technology. 2024; 14(03):1-10. Available from: https://journals.stmjournals.com/joaet/article=2024/view=176313
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| Volume | 14 |
| Issue | 03 |
| Received | 14/08/2024 |
| Accepted | 07/09/2024 |
| Published | 30/09/2024 |