ODE Solver

A web-based application for solving Ordinary Differential Equations (ODEs) using numerical methods. The application supports first-, second-, third-, and fourth-order ordinary differential equations and provides accurate numerical approximations, graphical visualization, solution tables, and Excel export.

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Live Demo

Application:
https://ode-solver-frontend.onrender.com

Backend API:
https://ode-solver-webapp.onrender.com

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Features

• Solve first-, second-, third-, and fourth-order ordinary differential equations.
• Supports the following numerical methods:
  • Euler Method
  • Improved Euler (Heun) Method
  • Fourth-Order Runge-Kutta (RK4)
  • Compare All Methods
• Interactive solution graphs.
• Numerical solution tables.
• Export computed solutions to Microsoft Excel (.xlsx).
• Mathematical equation preview using LaTeX.
• Built-in guide for supported mathematical functions.
• Responsive design for desktop, tablet, and mobile devices.
• Professional input validation and user-friendly error messages.

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Supported Mathematical Functions

The solver accepts the following mathematical functions and constants:

Function	Example
Sine	sin(x)
Cosine	cos(x)
Tangent	tan(x)
Exponential	exp(x)
Natural Logarithm	log(x)
Square Root	sqrt(x)
Absolute Value	abs(x)
Pi	pi

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Technologies Used

Frontend

• React.js
• React Router
• Plotly.js
• KaTeX
• XLSX
• CSS3

Backend

• Node.js
• Express.js
• Python
• SymPy

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Numerical Methods

The application implements the following numerical techniques:

• Euler Method
• Improved Euler (Heun) Method
• Fourth-Order Runge-Kutta (RK4)

These methods allow users to compare numerical approximations and evaluate the accuracy of different solution techniques.

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Installation

Clone the repository

git clone https://github.com/YamikaniWilliams/ode-solver-webapp.git

Frontend

cd frontend
npm install
npm start

Backend

cd backend
npm install
pip install -r requirements.txt
npm start

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How to Use

1. Select the order of the differential equation.
2. Enter the right-hand side function f(x, y, y′, y″, …, y⁽ⁿ⁻¹⁾).
3. Enter the initial conditions.
4. Specify the initial value of x, the final value of x, and the step size.
5. Choose a numerical method.
6. Click Compute Solution.
7. View the graph and numerical solution table.
8. Download the computed solution as an Excel file if required.

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Project Structure

ode-solver/
│
├── frontend/
│   ├── public/
│   ├── src/
│   └── package.json
│
├── backend/
│   ├── routes/
│   ├── services/
│   ├── parser.py
│   ├── solver.py
│   ├── server.js
│   ├── requirements.txt
│   └── package.json
│
├── LICENSE
└── README.md

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Future Improvements

Planned enhancements include:

• Systems of ordinary differential equations.
• Analytical (exact) solution support.
• Error analysis and convergence comparison.
• Dark mode.

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Author

Yamikani Williams

Email: odesolverapp@gmail.com

GitHub: https://github.com/YamikaniWilliams

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License

This project is licensed under the MIT License. See the LICENSE file for details.