Verified calculation capability

Ordinary differential equation Calculation Capability

Scalar first-order IVP y′=f(t,y) by Euler or RK4. rhs linear is y′=k y; poly is y′=p(t). Not rk45, not systems, not PDE, not CAS. · Math · Numerical

Capability ID math.numerical.ode · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Euler

Euler: y ← y + h f(t,y)
RK4: y ← y + (h/6)(k1+2k2+2k3+k4)

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`method`	—	—	input / output
`rhs`	—	—	input / output
`y0`	—	—	input / output
`t0`	—	—	input / output
`t1`	—	—	input / output
`n`	amount of substance	—	input / output
`k`	growth rate for y′=k y	—	input / output
`coeffs`	c0,c1,…,cn constant first for y′=p(t)	—	input
`h`	hydrogen-ion concentration	—	output
`y`	—	—	output
`exact`	—	—	output
`abs_err`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Scalar first-order only
Not rk45, not systems, not PDE, not CAS
Polynomial degree ≤ 8

Example

One numerical check. The calculator page holds worked steps and FAQ.

rk4 linear k=1 y0=1 t0=0 t1=1 n=40 → exact=e

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.0.0
Evidence tests: 9/9 calculation tests · golden 3/3 · boundary 2/2 · property 4/4
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)

Production attestation: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 163 remain CURRENT) @ 2026-09-19T00:00:17.039Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T21:41:55.460Z
Last production check: 2026-09-18T21:41:55.460Z
Public / cache: —
Origin: —

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 4/4.

Tool id: ordinary-differential-equation
Engine: ordinary-differential-equation
REST: POST /api/v1/calc/ordinary-differential-equation
MCP: execute_calculation with capability_id: "math.numerical.ode"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

ISO 80000-2:2019 Quantities and units — Mathematics

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.numerical.ode"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.0) when reproducibility matters. Full protocol notes: MCP docs.