DifferentialLab

Numerical ODE, difference equation, and PDE solver with a graphical interface for scientists, engineers, and students.

📖 Documentation • 🐛 Report Bug • 💡 Request Feature

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Features

• ODEs: Six methods (RK45, RK23, DOP853, Radau, BDF, LSODA) via SciPy
• Difference equations: Recurrence relations (geometric growth, logistic map, Fibonacci, etc.)
• PDEs: 2D elliptic solver (Poisson, Laplace) plus general operator-based PDEs with configurable derivative terms
• Vector ODEs: Coupled systems with animation, 3D phase-space trajectories, and surface visualization
• Unified f-notation: Write equations using f[0] (function), f[1] (first derivative), f[i,k] (component i, derivative k for vector ODEs)
• Predefined equations: Harmonic oscillator, pendulum, Van der Pol, Lorenz, Lotka-Volterra, Duffing, Schrödinger, and more
• Function transforms: Fourier (FFT), Laplace, Taylor series, Hilbert, Z-transform
• Custom equations: Write any ODE, difference equation, or PDE in Python syntax
• Interactive result tabs: Select derivatives to plot, choose phase-space axes, switch visualization modes without re-solving
• Professional plots: Solution curves, phase portraits (2D/3D), surface/contour, vector animation
• Statistics: Mean, max/min, period, energy, RMS, residual error metrics
• Export: CSV, JSON, PNG/JPG/PDF, MP4 animation
• Configurable via .env file or in-app Configuration dialog
• Desktop GUI built with Tkinter/ttk

Requirements

• Python 3.12 or higher
• Windows 10/11, macOS 10.14+, or Linux
• 4 GB RAM minimum

Quick Start

Installation (first-time setup)

Windows:

install.bat

Linux/macOS:

chmod +x install.sh
./install.sh

This clones the repository (if needed) and runs setup.

Manual setup (existing clone)

1. Create virtual environment and install dependencies:

# Windows
bin\setup.bat

# Linux/macOS
chmod +x bin/setup.sh
./bin/setup.sh

2. Run the application:

# Windows
bin\run.bat

# Linux/macOS
./bin/run.sh

Or run directly:

python src/main_program.py

Configuration

Copy .env.example to .env and customize, or use the in-app Configuration dialog.

Available settings:

• UI theme (colors, fonts, padding)
• Plot style (line, markers, fonts, grid)
• Solver defaults (method, tolerances)
• File paths and output format
• Logging

Documentation

Full documentation is built with Sphinx and hosted on Read the Docs.

To build the docs locally:

pip install -e ".[docs]"
cd docs
make html          # Linux/macOS
make.bat html      # Windows

The output will be in docs/_build/html/.

Documentation contents:

• Getting Started — installation, setup, first run
• User Guide — walk-through of the complete workflow
• Configuration Reference — every .env setting explained
• Architecture — module structure and design decisions
• API Reference — auto-generated from source docstrings

Dependencies

Package	Version	Purpose
NumPy	>= 2.0	Numerical computations
Matplotlib	>= 3.10	Plotting and visualization
SciPy	>= 1.15	ODE solving engine
python-dotenv	>= 1.0	Environment configuration
PyYAML	>= 6.0	Equation definitions

License

MIT License. See license.md.

Third-party licenses: see THIRD_PARTY_LICENSES.md.

Author

Alejandro Mata Ali