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GE: Numerical Methods - Practicals

Course

Welcome to the collection of practical assignments for the Numerical Methods course. This repository contains implementations for various numerical algorithms using Wolfram Mathematica.

🛠️ Environment Setup

This project uses Wolfram Language (.nb formats). To run these programs, you need a environment that support Wolfram Mathematica code.

Quick Setup:

  1. Wolfram Mathematica: Download and install from wolfram.com.
  2. Wolfram Cloud (Free Alternative): You can also run these notebooks online via Wolfram Cloud.
  3. Loading the File: Open GE Practical.nb in Mathematica or reference the code in GePractical.md.

📅 List of Practicals

The following methods are implemented and detailed in GePractical.md:

1️⃣ Solution of Transcendental & Algebraic Equations

  • Bisection Method - Finding roots by repeatedly bisecting an interval (3 Variations).
  • Secant Method - Root-finding using secant lines (2 Variations).
  • Regula Falsi (Regular Falsi) - Root-finding using linear interpolation and falsi position.
  • Newton-Raphson Method - Finding roots using tangents and automatic differentiation (2 Variations).

2️⃣ Solution of Linear Algebraic Equations

  • Gauss-Jacobi Method - Iterative solver with support for standard and Matrix Form (GaussJacobiMatrixForm).
  • Gauss-Seidel Method - Improved iterative solver with standard and Matrix Form (GaussSeidelMatrixForm).

3️⃣ Interpolation

  • Lagrange Interpolation - Polynomial interpolation with support for plotting and comparison with built-in functions.
  • Newton's Divided Difference - Implementation of Divided Difference tables and Polynomial construction (NDD/NDDP).

4️⃣ Numerical Integration

  • Trapezoidal Rule - Composite Trapezoidal rule with error verification against true integrals.
  • Simpson's Rule - Composite Simpson's 1/3rd rule with input validation for even sub-intervals.

5️⃣ Numerical Solution of Ordinary Differential Equations

  • Euler's Method - Solving ODEs using fixed number of steps or fixed step size h.
  • 2nd Order Runge-Kutta (Modified Euler) - More accurate ODE solver with built-in comparison to exact solutions.

<p align="right">

<i>Developed with ❤️ by <a href="https://github.com/16ratneshkumar">16ratneshkumar</a></i>

</p>

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