differentiation-schemes
Select and apply numerical differentiation schemes for PDE/ODE discretization. Use when choosing finite difference/volume/spectral schemes, building stencils, handling boundaries, estimating truncation error, or analyzing dispersion and dissipation.
npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill differentiation-schemes --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Differentiation Schemes ## Goal Provide a reliable workflow to select a differentiation scheme, generate stencils, and assess accuracy for simulation discretization. ## Requirements - Python 3.8+ - NumPy (for stencil computations) - No heavy dependencies ## Inputs to Gather | Input | Description | Example | |-------|-------------|---------| | Derivative order | First, second, etc. | `1` or `2` | | Target accuracy | Order of truncation error | `2` or `4` | | Grid type | Uniform, nonuniform | `uniform` | | Boundary type | Periodic, Dirichlet, Neumann | `periodic` | | Smoothness | Smooth or discontinuous | `smooth` | ## Decision Guidance ### Scheme Selection Flowchart ``` Is the field smooth? ├── YES → Is domain periodic? │ ├── YES → Use central differences or spectral │ └── NO → Use central interior + one-sided at boundaries └── NO → Are there shocks/discontinuities? ├── YES → Use upwind, TVD, or WENO └── NO → Use central with limiters ``` ### Quick Reference | Situation | Recommended Scheme | |-----------|-------------------| | Smooth, periodic | Central, spectral | | Smooth, bounded | Central + one-sided BCs | | Advection-dominated | Upwind | | Shocks/fronts | TVD, WENO | | High
- Goal
- Requirements
- Inputs to Gather
- Decision Guidance
- Scheme Selection Flowchart
- Quick Reference
- Script Outputs (JSON Fields)
- Workflow
- Conversational Workflow Example
- Pre-Discretization Checklist
- CLI Examples
- Error Handling
- Interpretation Guidance
- Stencil Properties
python3 scripts/scheme_selector.py --smooth --periodic --order 2 --accuracy 4 --json python3 scripts/stencil_generator.py --order 2 --accuracy 4 --scheme central --json Select scheme for smooth periodic problem python3 scripts/scheme_selector.py --smooth --periodic --order 1 --accuracy 4 --json Generate central difference stencil for first derivative python3 scripts/stencil_generator.py --order 1 --accuracy 2 --scheme central --json Generate 4th-order second derivative stencil Estimate truncation error python3 scripts/truncation_error.py --dx 0.01 --order 2 --accuracy 2 --scale 1.0 --json
What does the differentiation-schemes skill do?
Select and apply numerical differentiation schemes for PDE/ODE discretization. Use when choosing finite difference/volume/spectral schemes, building stencils, handling boundaries, estimating truncation error, or analyzing dispersion and dissipation.
How do I install it?
Run `npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill differentiation-schemes --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From FreedomIntelligence/OpenClaw-Medical-Skills, a repository with 2,909 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.