Numerical Methods

Finding the solutions of the mahematical equations in an iterative method is a cumbersome task. It takes a lot of time to compute the value repeatedly in hand and there is a high chance of getting wrong answers too.

So, this website demonstrates different iterative numerical methods to solve a single equation as well as system of equations upto 100 iterations instantly.

Table of Contents

• Getting Started
• Repository Structure
• Different Methods Used
• Libraries/Tools Used
• Contributing
• Acknowledgements
• License

Getting Started

1. Fork the repository.
2. Clone the repository.

git clone [email protected]:<username>/numerical-methods.git  

3. Go to the directory.

cd numerical-methods

4. Install npm libraries. It will take some time to download all the libraries.

npm install

5. Run the website in local machine.

npm start

Repository Structure

The file structure is very similar to any other React file structure except src folder.

The src folder contains

src
├── components
    ├── <contains-input-components>
    ├── one_var_eqn.jsx
    ├── three_var_eqn.jsx
├── methods
    ├── <contains-all-iterative-methods>
    ├── GaussSeidel.jsx
    ├── GeneralIterative.jsx
    ├── NewtonRaphson.jsx
├── styles
    ├── <contains-stylesheet>
    ├── App.css
    ├── index.css
    ├── equations_gim.css
    ├── equations_gs.css
    ├── header.css

Different Methods Used

Till now, three methods are added. Expand the name for the details.

Gauss-Seidel Method

In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations.

General-Iterative Method

"The General Iteration Method" also known as "The Fixed Point Iteration Method" , uses the definition of the function itself to find the root in a recursive way.

Note: First write the equation in the form of x=ϕ(x).

Newton-Raphson Method

In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots of a real-valued function.

Libraries/Tools Used

1. ReactJS is used for the front-end.
2. All the algorithms are present in src>methods folder, written in JS.
3. math.js is also used in different methods for rounding off values, differentiation, etc.
4. CSS for styling the pages.

Netlify is used to deploy the page.

Contributing

New methods/bug fixes/UI fixes are always welcome. Make a new issue with a proper heading and description. It will be easy to discuss further and make a PR for the same issue.

Acknowledgements

1. ReactJS used under the terms of MIT License, Copyright (c) Facebook, Inc. and its affiliates.
2. mathjs used under the terms of Apache License 2.0.
3. Navbar style inspired from this blog.

License

Licensed Under MIT License

Copyright (c) 2022 Subhendu Dash