Author: Avrojit Joydhar (IMS23068)
Duration: May 2024 – April 2025
This report presents a comprehensive study of Numerical Analysis, emphasizing the development, implementation, and analysis of numerical methods used to solve differential equations. It covers both Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs), highlighting their computational treatment and practical applications.
- Chapter 1: Introduction
- Chapter 2: Numerical Solutions of ODEs (IVP/BVP, Picard, Euler, RK methods)
- Chapter 3: Error Analysis and Order of Convergence
- Chapter 4: Partial Differential Equations
- Chapter 5: Boundary Value Problems (Dirichlet, Neumann, Robin)
- Chapter 6: Fourier Series (Real, Complex, and Magnitude-Angle Forms)
- Chapter 7: Finite Element Methods (Galerkin Method, Mesh Implementation)
The report features code implementations for various numerical techniques in C++ and Python, including:
- Euler's Method & Modified Euler
- Runge-Kutta (RK2, RK3, RK4)
- Adams Predictor-Corrector
- Fourier Series plotting
- Finite Element Method (1D Poisson Equation)
- Mesh generation using Matplotlib and Gnuplot
💻 All source code is available at:
https://github.com/avroj1t/Numerical-Analysis
- Motivation for using numerical methods when analytical solutions are infeasible
- Comparative analysis of single-step vs. multi-step approaches
- Discussion of error control, convergence, and stability
- Real-world relevance to simulation, modeling, and engineering systems
- Application of Fourier and FEM for solving complex boundary problems
See Chapter 8 of the report for a complete list of academic references and resources used throughout this project.
This project was completed as part of academic work from May 2024 to April 2025.