ODE VAS (Ordinary Differential Equation Visualization and Analysis System) is a powerful, modern web-based platform for solving, visualizing, and analyzing first-order ordinary differential equations. It combines analytical methods with numerical techniques to provide comprehensive insights into ODE behavior, stability, and convergence.

• Try it here : link

• Demo video of the project : Video

Fast numerical solutions with tabular output. Select a method (Euler, RK4, or analytical methods like Separation of Variables), enter your equation, set initial conditions, and solve.

Real-time graphing with dynamic controls:

• Visualize solutions with smooth curve plotting
• Enable slope fields (direction fields) with customizable density, color, and opacity
• Use interactive sliders to adjust y₀ and x_end with instant graph updates
• View live statistics: max/min values, final points, and solution behavior

Comprehensive ODE analysis with multiple tools:

• Parameter Variation: Compare solutions across parameter ranges with color-coded multi-line graphs
• Step-Size Comparison: Analyze convergence rates and error metrics across different step sizes
• Stability Analysis: Automatic equilibrium point detection with stability classification (stable/unstable/neutral)
• Phase Portrait: Generate flow fields with 7 trajectories from different initial conditions

• Numerical: Euler, Improved Euler, Runge-Kutta 4th Order (RK4)
• Analytical: Direct Integration, Separation of Variables, Integrating Factor, Substitution

• Exponential Decay: -2*x*y
• Logistic Growth: y*(1-y)
• Harmonic Oscillator: -x/y
• Polynomial: x**2 - y
• Trigonometric: sin(x)*y
• Exponential Function: exp(-x)*y

sin, cos, tan, exp, log, sqrt, +, -, *, /, ** (power)

Compare solutions across different parameter values (e.g., varying decay rates or growth constants). Results displayed as color-coded multi-line graphs with HSL gradient coloring.

Analyze numerical accuracy by comparing solutions with different step sizes. View:

• Number of evaluation points
• Maximum and mean errors (compared to reference)
• Convergence rates between consecutive step sizes

Automatically finds equilibrium points by solving dy/dx = 0. Classifies stability based on derivative:

• Stable: f'(y) < 0 (solutions converge)ge)
• Unstable: f'(y) > 0 (solutions diverge)ge)
• Neutral: f'(y) = 0 (center/saddle point)

Generates 7 trajectories from different starting points across the domain. Displays equilibrium lines as dashed horizontals with color-coded stability.

• Real-Time Validation: Input fields validate as you type with visual feedback
• Glassmorphism Design: Modern blur effects on panels and controls
• Toast Notifications: Non-intrusive feedback for actions
• Responsive Layout: Works on desktop, tablet, and mobile
• Dark Theme: Easy on the eyes with red accent colors
• Keyboard Shortcuts: ESC to close modals
• Form Persistence: Restore previous analysis with one click

• Flask - Web framework
• SymPy - Symbolic mathematics and analytical solving
• NumPy - Numerical computations

• HTML5 / CSS3 - Modern responsive UI with glassmorphism effects
• JavaScript (ES6) - Interactive controls and real-time updates
• Chart.js - High-performance data visualization

• Red/Black theme with glassmorphism
• Smooth transitions and animations
• Mobile-responsive layout

1. Prerequisites:

   • Python 3.8 or higher
   • Modern Web Browser (Chrome, Firefox, Edge, Safari)

2. Clone the Repository:

   git clone https://github.com/aarvo09/ODE-VAS
   
   cd "ODE VAS"

3. Install Dependencies:

   pip install -r requirements.txt

4. Run the Application:

   python app.py

5. Access the Application:

   • Open your browser and navigate to: http://localhost:5000

ODE VAS/
├── .venv/                     
├── static/
│   ├── images/
│   │   └── math_doodles.png
│   ├── js/
│   │   ├── advanced.js
│   │   ├── quick-solver.js
│   │   ├── utils.js
│   │   └── visualizer.js
│   ├── advanced.css
│   ├── home.css
│   ├── quick-solver.css
│   ├── style.css
│   ├── transitions.css
│   └── visualizer.css
├── templates/
│   ├── advanced.html
│   ├── help.html
│   ├── home.html
│   ├── quick-solver.html
│   ├── solver.html
├── .gitignore
├── app.py
├── LICENSE
├── README.md
└── requirements.txt                  
nts.txt                  

##  License

This project is open source and available under the MIT License.

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##  Author

**Arvind**
- GitHub: [https://github.com/aarvo09]
- Email: [[email protected]]

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