DifferentialLab

Numerical ODE, difference-equation, and PDE solver with a desktop GUI for science and engineering workflows.

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What It Solves

• ODEs with SciPy integrators (RK45, RK23, DOP853, Radau, BDF, LSODA)
• Difference equations (recurrence systems)
• PDEs (elliptic 2D solver and operator-based PDE workflows)
• Vector ODE systems with dedicated visualization modes
• Function transforms (Fourier, Laplace, Taylor, Hilbert, Z-transform)

Core Features

• Predefined equation catalog loaded from YAML (config/equations/*.yaml)
• Custom equation parsing with safe AST validation
• Unified f[...] notation (f[0], f[1], f[i,k])
• Interactive result dialogs (derivative selection, phase-space selection, dynamic redraw)
• Export to CSV, JSON, static figures, and MP4 animations
• Configurable UI/plot/solver behavior via .env or in-app configuration dialog

Complex Problems (Plugin Mode)

Complex Problems is a plugin-style subsystem for specialized models with custom UI, solver, and result dialogs.

Current modules:

• coupled_oscillators (1D coupled oscillators and FPUT variants)
• membrane_2d (2D coupled nonlinear membrane)
• nonlinear_waves (NLSE and KdV)
• schrodinger_td (time-dependent Schrodinger in 1D/2D)
• antenna_radiation (far-field patterns and antenna metrics)
• aerodynamics_2d (2D incompressible obstacle flow approximations)
• pipe_flow (steady and transient 1D pipe-flow models)

Requirements

• Python >=3.12
• Windows 10/11, macOS, or Linux
• Tkinter available in the Python runtime (GUI requirement)

Quick Start

First-time setup

Windows:

install.bat

Linux/macOS:

chmod +x install.sh
./install.sh

Existing clone

Windows:

bin\setup.bat
bin\run.bat

Linux/macOS:

chmod +x bin/setup.sh bin/run.sh
./bin/setup.sh
./bin/run.sh

Direct run:

python src/main_program.py

Installed console entry point:

differential-lab

Documentation

• Documentation Home
• Getting Started
• User Guide
• Complex Problems Guide
• Configuration Reference
• Architecture
• Developer Guide
• Testing
• API Reference

To build docs locally:

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

Output directory: docs/_build/html/.

Development

Install development dependencies:

pip install -e ".[dev]"

Run tests:

pytest

Contribution guide: CONTRIBUTING.md.

License

MIT License. See license.md.

Third-party licenses: THIRD_PARTY_LICENSES.md.