STM Journals Peer-reviewed research from Consortium e-Learning Network

Journal of Aerospace Engineering & Technology Original Research

Numerical Solution of Ordinary Differential Equation and Solution of Partial Differential Equation

  1. Ryan Nadar Aerospace Engineering, Ajeenkya DY Patil University, Charholi Budruk, Pune
  2. Shirish Kulkarni Department of Mathematics, Ajeenkya DY Patil University, Charholi Budruk, Pune

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. ODEs and 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-Kutta 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 method, Runge-Kutta methods for ODEs, finite difference method (FDM), finite element method (FEM), and finite volume method (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 provide increasingly accurate and effective answers to practical issues.

Keywords

References (38)

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