Is numerical-integration safe to install?

SaferSkills independently audited numerical-integration (Agent Skill) and scored it 100/100 (green). The audit ran 55 deterministic rules across Security, Supply Chain, Maintenance, Transparency, and Community; it found 0 high-severity and 0 lower-severity findings. The full rule-by-rule trace and per-finding evidence are below. Free, methodology-open.

CategoryWeightCategory scoreContribution

Securityprompt, exec, net, exfil, eval

35%

100

35.0 pts

Supply chainhash, typosquat, maintainer, lockfile

20%

100

20.0 pts

Maintenancestaleness, pinning, CI

15%

100

15.0 pts

TransparencySKILL.md, perms, README

15%

100

15.0 pts

Communityinstalls, verify, response

15%

100

15.0 pts

Findings & checks · 0 flagged

Securityscore 100 · 0 findings

✓—All security checks passedNo findings in this category for the latest scan.pass

Supply chainscore 100 · 0 findings

✓—All supply chain checks passedNo findings in this category for the latest scan.pass

Maintenancescore 100 · 0 findings

✓—All maintenance checks passedNo findings in this category for the latest scan.pass

Transparencyscore 100 · 0 findings

✓—All transparency checks passedNo findings in this category for the latest scan.pass

Communityscore 100 · 0 findings

✓—All community checks passedNo findings in this category for the latest scan.pass

The primary manifest — the file an agent reads to learn what this artifact does.

skills/numerical-integration/SKILL.md · 1 file

skills/numerical-integration/SKILL.md6.1 KB · Markdown

name: numerical-integration

description: Select and configure time integration methods for ODE/PDE simulations. Use when choosing explicit/implicit schemes, setting error tolerances, adapting time steps, diagnosing integration accuracy, planning IMEX splitting, or handling stiff/non-stiff coupled systems.

allowed-tools: Read, Bash, Write, Grep, Glob

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)

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.py for 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

Conversational Workflow Example

User: I'm solving the Allen-Cahn equation with a stiff double-well potential. What integrator should I use?

Agent workflow:

Check integrator options:

   python3 scripts/integrator_selector.py --stiff --jacobian-available --accuracy high --json

Plan the IMEX splitting (diffusion implicit, reaction explicit):

   python3 scripts/imex_split_planner.py --stiff-terms diffusion --nonstiff-terms reaction --coupling weak --json

Recommend: Use IMEX-BDF2 with diffusion term implicit, double-well reaction explicit.

Pre-Integration Checklist

[ ] Identify stiffness and dominant time scales
[ ] Set rtol/atol consistent with physics and units
[ ] Confirm integrator compatibility with stiffness
[ ] Use error norm to accept/reject steps
[ ] Verify convergence with tighter tolerance run

CLI Examples

# Select integrator for stiff problem with Jacobian
python3 scripts/integrator_selector.py --stiff --jacobian-available --accuracy high --json

# Compute scaled error norm
python3 scripts/error_norm.py --error 0.01,0.02 --solution 1.0,2.0 --rtol 1e-3 --atol 1e-6 --json

# Adaptive step control with PI controller
python3 scripts/adaptive_step_controller.py --dt 1e-2 --error-norm 0.8 --order 4 --controller pi --json

# Plan IMEX splitting
python3 scripts/imex_split_planner.py --stiff-terms diffusion,elastic --nonstiff-terms reaction --coupling strong --json

# Estimate splitting error
python3 scripts/splitting_error_estimator.py --dt 1e-4 --scheme strang --commutator-norm 50 --target-error 1e-6 --json

Error Handling

Error	Cause	Resolution
`rtol and atol must be positive`	Invalid tolerances	Use positive values
`error-norm must be positive`	Negative error norm	Check error computation
`Unknown controller`	Invalid controller type	Use `i`, `pi`, or `pid`
`Splitting requires at least one term`	Empty term list	Specify stiff or nonstiff terms

Interpretation Guidance

Error Norm Values

Error Norm	Meaning	Action
< 1.0	Step acceptable	Accept, maybe increase dt
≈ 1.0	At tolerance boundary	Accept with current dt
> 1.0	Step rejected	Reject, reduce dt

Controller Selection

Controller	Properties	Best For
I (integral)	Simple, some overshoot	Non-stiff, moderate accuracy
PI (proportional-integral)	Smooth, robust	General use
PID	Aggressive adaptation	Rapidly varying dynamics

IMEX Strategy

Coupling	Strategy
Weak	Simple operator splitting
Moderate	Strang splitting
Strong	Fully coupled IMEX-RK

Limitations

No automatic stiffness detection: Use stiffness_detector from numerical-stability
Splitting assumes separability: Terms must be cleanly separable
Jacobian requirement: Some methods need analytical or numerical Jacobian

References

references/method_catalog.md - Integrator options and properties
references/tolerance_guidelines.md - Choosing rtol/atol
references/error_control.md - Error norm and adaptation formulas
references/imex_guidelines.md - Stiff/non-stiff splitting
references/splitting_catalog.md - Operator splitting patterns
references/multiphase_field_patterns.md - Phase-field specific splits

Version History

v1.1.0 (2024-12-24): Enhanced documentation, decision guidance, examples
v1.0.0: Initial release with 5 integration scripts

numerical-integration— agent skill

Is numerical-integration safe to install?

Numerical Integration

Goal

Requirements

Inputs to Gather

Decision Guidance

Choosing an Integrator

Stiff vs Non-Stiff Detection

Script Outputs (JSON Fields)

Workflow

Conversational Workflow Example

Pre-Integration Checklist

CLI Examples

Error Handling

Interpretation Guidance

Error Norm Values

Controller Selection

IMEX Strategy

Limitations

References

Version History

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