Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add HeshamFS/materials-simulation-skills --skill differentiation-schemesgit clone --depth 1 https://github.com/HeshamFS/materials-simulation-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/heshamfs/materials-simulation-skills/differentiation-schemes)<a href="https://agentmods.dev/skills/heshamfs/materials-simulation-skills/differentiation-schemes"><img src="https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/differentiation-schemes/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/heshamfs/materials-simulation-skills/differentiation-schemes"><img src="https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/differentiation-schemes.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00125 | $0.03250 |
| Opus 5.5 | $0.00050 | $0.01300 |
| Sonnet 5.5 | $0.00025 | $0.00650 |
| Haiku 4.5 | $0.00013 | $0.00325 |
Grade A, and why
differentiation-schemes scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 5d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 242 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Differentiation Schemes
Goal
Provide a reliable workflow to select a differentiation scheme, generate stencils, and assess accuracy for simulation discretization.
Requirements
- Python 3.10+
- 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 accuracy needed | Compact (Padé), spectral |
Script Outputs (JSON Fields)
| Script | Key Outputs |
|---|---|
scripts/stencil_generator.py |
offsets, coefficients, order, accuracy, scheme |
scripts/scheme_selector.py |
recommended, alternatives, notes |
scripts/truncation_error.py |
error_scale, order, reduction_if_halved |
Workflow
- Identify requirements - derivative order, accuracy, smoothness
- Select scheme - Run
scripts/scheme_selector.py - Generate stencils - Run
scripts/stencil_generator.py - Estimate error - Run
scripts/truncation_error.py - Validate - Test with manufactured solutions or grid refinement
Conversational Workflow Example
User: I need to discretize a second derivative for a diffusion equation on a uniform grid. I want 4th-order accuracy.
What ships with it
9 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
- CHANGELOG.md 3.3 KB
- evals/evals.json 6.0 KB
- references/boundary_handling.md 7.3 KB
- references/error_guidance.md 7.0 KB
- references/scheme_selection.md 6.7 KB
- references/stencil_catalog.md 6.2 KB
- scripts/scheme_selector.py 3.5 KB runs code
- scripts/stencil_generator.py 5.2 KB runs code
- scripts/truncation_error.py 2.1 KB runs code
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 5d ago Changed · +2 lines dfb1517850dc
- 1mo ago First seen · 240 lines · 125 tokens per session scan A 1a0c442c91ee
differentiation-schemes is a skill published in the GitHub repository HeshamFS/materials-simulation-skills (83 stars, last pushed 6d ago), licensed Apache-2.0. It adds 125 tokens to every session and 3,250 once invoked, about $0.0005 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
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