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 numerical-integrationgit 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/numerical-integration)<a href="https://agentmods.dev/skills/heshamfs/materials-simulation-skills/numerical-integration"><img src="https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/numerical-integration/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/numerical-integration"><img src="https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/numerical-integration.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 | $0.00142 | $0.03387 |
| Opus 5.5 | $0.00057 | $0.01355 |
| Sonnet 5.5 | $0.00028 | $0.00677 |
| Haiku 4.5 | $0.00014 | $0.00339 |
Grade A, and why
numerical-integration 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 4d 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 — 248 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Numerical Integration
Goal
Provide a reliable workflow to select integrators, set tolerances, and manage adaptive time stepping for time-dependent simulations.
Requirements
- Python 3.10+
- 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)
| Script | Key Outputs |
|---|---|
scripts/error_norm.py |
error_norm, scale_min, scale_max |
scripts/adaptive_step_controller.py |
accept, dt_next, factor |
scripts/integrator_selector.py |
recommended, alternatives, notes |
scripts/imex_split_planner.py |
implicit_terms, explicit_terms, splitting_strategy |
scripts/splitting_error_estimator.py |
error_estimate, substeps |
Workflow
- Classify stiffness - Check eigenvalue spread or use stiffness_detector
- Choose tolerances - See
references/tolerance_guidelines.md - Select integrator - Run
scripts/integrator_selector.py - Compute error norms - Use
scripts/error_norm.pyfor step acceptance - Adapt step size - Use
scripts/adaptive_step_controller.py - Plan IMEX/splitting - If mixed stiff/nonstiff, use
scripts/imex_split_planner.py - Validate convergence - Repeat with tighter tolerances
What ships with it
13 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 3.2 KB
- evals/evals.json 7.0 KB
- references/error_control.md 8.0 KB
- references/imex_guidelines.md 7.5 KB
- references/method_catalog.md 5.9 KB
- references/multiphase_field_patterns.md 7.5 KB
- references/splitting_catalog.md 7.7 KB
- references/tolerance_guidelines.md 6.9 KB
- scripts/adaptive_step_controller.py 5.5 KB runs code
- scripts/error_norm.py 5.7 KB runs code
- scripts/imex_split_planner.py 5.4 KB runs code
- scripts/integrator_selector.py 5.3 KB runs code
- scripts/splitting_error_estimator.py 3.1 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.
- 4d ago Changed · +4 lines 7f16af94606f
- 1mo ago First seen · 244 lines · 142 tokens per session scan A 09d21f695bc9
numerical-integration is a skill published in the GitHub repository HeshamFS/materials-simulation-skills (83 stars, last pushed 5d ago), licensed Apache-2.0. It adds 142 tokens to every session and 3,387 once invoked, about $0.0006 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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