Numerical Integration
Goal
Provide a reliable workflow to select integrators, set tolerances, and manage adaptive time stepping for time-dependent simulations.
Requirements
- Python 3.8+
- NumPy (for some scripts)
- No heavy dependencies for core functionality
Inputs to Gather
| Input | Description | Example |
|---|
| Problem type | ODE/PDE, stiff/non-stiff | stiff PDE |
| Jacobian available | Can compute ∂f/∂u? | yes |
| Target accuracy | Desired error level | 1e-6 |
| Constraints | Memory, implicit allowed? | implicit OK |
| Time scale | Characteristic time | 1e-3 s |
Decision Guidance
Choosing an Integrator
Is the problem stiff?
├── YES → Is Jacobian available?
│ ├── YES → Use Rosenbrock or BDF
│ └── NO → Use BDF with numerical Jacobian
└── NO → Is high accuracy needed?
├── YES → Use RK45 or DOP853
└── NO → Use RK4 or Adams-Bashforth
Stiff vs Non-Stiff Detection
| Symptom | Likely Stiff | Action |
|---|
| dt shrinks to tiny values | Yes | Switch to implicit |
| Eigenvalues span many decades | Yes | Use BDF/Radau |
| Smooth solution, reasonable dt | No | Stay explicit |
Script Outputs (JSON Fields)
