Ready to supercharge your AI agents?

Install any skill in seconds. Free to start, no credit card required.

Get Started Free →

Boundary Value Problems · vibeeval | DecimalAI

scienceby vibeeval

Boundary Value Problems

vibeeval/boundary-value-problems

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for boundary value problems in odes pdes

SkillScore100Maintained

Automatic

Research pack

Last verified 8/4/2026

What it changes

Passed 23 of 23 test cases with the skill, and 22 of 23 without it.

Without skill96%

With skill100%

Checks it passed that the model alone missed

uses solve_bvp to compute the solution for the boundary value problem

1 fixed22 passed either way0 still failing0 broke

Pass-rate lift: +4 pp
Tokens: +37%
Agent turns: 0%
Response time: -21%

Model gemini-3.6-flashMeasured 8/4/2026v123 of 23 cases passed with skill

Tokens, turns and time describe resource use, not a dollar price.

Use this skill

Save it into your project's skills folder. Claude Code picks it up in its next session.

curl -fsSL --create-dirs -o .claude/skills/vibeeval-boundary-value-problems/SKILL.md https://app.decimal.ai/s/vibeeval-boundary-value-problems/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-boundary-value-problems, and start Claude Code with claude --plugin-dir "$(git rev-parse --show-toplevel)/.agents"

1 · One-time — install the CLI (docs ↗)

pip install "decimalai>=0.15"

2 · Get the skill — writes .agents/skills/vibeeval-boundary-value-problems/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-boundary-value-problems

No CLI? Get the same file — curl · raw file

curl -fsSL --create-dirs -o .claude/skills/vibeeval-boundary-value-problems/SKILL.md https://app.decimal.ai/s/vibeeval-boundary-value-problems/SKILL.md

Raw file: /s/vibeeval-boundary-value-problems/SKILL.md ↗ · machine-readable summary at /s/vibeeval-boundary-value-problems.json ↗

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

A test case the skill fixed. Same model, same prompt, with and without the skill.

Prompt

I'm working on a second-order nonlinear differential equation y'' + sin(y) = 0 over the domain x from 0 to 1, with boundary conditions y(0) = 0 and y(1) = 0.5. Could you set up and run a numerical boundary-value solver to find the solution curve across this interval and evaluate y at x = 0.5?

What was checked, without and with the skill
Checked	Without skill	With skill
uses solve_bvp to compute the solution for the boundary value problem	Missed	Passed
provides the evaluated solution value at x equal to 0.5	Passed	Passed

case-01 · gemini-3.6-flash · 8/4/2026 · answers are capped and redacted

What's inside

The instructions your model reads when the skill loads.

SKILL.md68 linessingle file

Boundary Value Problems

When to Use

Use this skill when working on boundary-value-problems problems in odes pdes.

Decision Tree

Problem Classification
- Two-point BVP: conditions at x=a and x=b?
- Sturm-Liouville: eigenvalue problem?
- Mixed conditions: Dirichlet, Neumann, Robin?
Shooting Method
- Convert BVP to IVP
- Guess missing initial conditions
- Iterate to satisfy boundary conditions
- scipy.integrate.solve_ivp + root finding
Finite Difference Method
- Discretize domain: x_i = a + i*h
- Replace derivatives with differences: y'' ~ (y_{i+1} - 2y_i + y_{i-1})/h^2
- Solve resulting linear system
- sympy_compute.py linsolve "tridiagonal_matrix" "boundary_vector"
Collocation/BVP Solver
- scipy.integrate.solve_bvp(ode, bc, x, y_init)
- Provide initial mesh and guess
- Check residual for accuracy
Eigenvalue Problems
- Sturm-Liouville form: -(p(x)y')' + q(x)y = lambda*w(x)*y
- Eigenvalues are real if p, w > 0
- Eigenfunctions orthogonal with weight w
- sympy_compute.py eigenvalues "sturm_liouville_matrix"

Tool Commands

Track record

Benchmark

23 / 23

test cases passed, vs 22 / 23 without

Adoption

Users: 2
Times used: 27

Safety and source details

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

View 15 scanner checks

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

skills/math/odes-pdes/boundary-value-problems/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

Other skills for the same job

Published skills whose descriptions closely match this one, with their headline benchmark lift.

vibeeval/second-order-odesProblem-solving strategies for second order odes in odes pdesClose match+14 pp pass-rate lift

More skills from the same source and nearby in the registry, with their headline benchmark lift.

Ready to supercharge your AI agents?

See it in action

What's inside

Boundary Value Problems

When to Use

Decision Tree

Tool Commands

Track record

Benchmark

Adoption

SkillSafety

Source

Other skills for the same job

Related skills