ODE Solver Web Application

Overview

This project is a web-based Ordinary Differential Equation (ODE) solver built with Python Flask. It currently supports Euler’s method for solving first-order ODEs and provides graphical and tabular results.

Features

• Input any first-order ODE in the form dy/dx = f(x,y) via a user-friendly web form.
• Specify initial conditions (x0, y0), step size (h), and final x value.
• Generates solution plot dynamically using Matplotlib.
• Displays results in a well-formatted table.
• Allows saving results to CSV (exports/results.csv).
• Responsive and clean UI with CSS styling.
• Button to easily solve another equation without reloading the page.

Requirements

• Python 3.x
• Flask
• Matplotlib
• Other dependencies listed in requirements.txt

Installation

Clone the repo

git clone https://github.com/your-username/ode-solver-web.git
cd ode-solver-web

Create virtual environment

python -m venv venv
venv\Scripts\activate     # for Windows

or

source venv/bin/activate  # for Mac/Linux
run command deactivate for deactivating virtual environment.

Install requirements

pip install -r requirements.txt

Run the app

python app.py

Open http://127.0.0.1:5000 in your browser.

Folder Structure

ode-solver-web/
├── app.py                     # Main Flask app
├── solver.py                  # Contains the Euler method function
├── utils.py                   # Contains plotting utilities
├── config.py                  # Optional config/settings (like secret key)
├── templates/
│ ├── form.html                # HTML form for user input
│ └── index.html               # Results page
├── static/
│ └── style.css                # CSS styling
├── exports/
│ ├── results.csv              # CSV file for results
│ └── static/
│ └── output.png               # Generated plot image
├── requirements.txt           # Project dependencies
├── README.md                  # This file
└── .gitignore, .gitattributes # Git config files

Usage

Fill out the ODE equation, initial conditions, and step size in the form.
Click Solve to view the results.
A plot and data table will be generated and displayed.
Option to Solve another equation with the button on the results page.

Instructor

- Project supervised by:
- Mr. Harish Bhandari

🔍 Example Input

Equation: dy/dx = x + y
x0 = 0
y0 = 1
h = 0.1
xf = 1
Method: Euler

Project Members

• Homraj Shahi
• Atul HUmagain
• Abishekh Joshi
• Shreyash Mahato
• Sugam Mahara