ODE Solver (Euler / RK4 / RK45) implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-clean

Evidence ID

t6-026

Effect

Computation or source lookup only

Input and validation requirements

• A zero, negative, NaN, or excessively large step size can cause invalid progression or nontermination unless explicitly rejected.
• Adaptive control can divide by zero or produce an undefined next step when the estimated error is zero; the implementation needs a defined zero-error step-growth rule and a maximum step size.
• Absolute-only error control can accept poor results for large-magnitude states, while relative-only control can fail near zero; the error norm and scaling must be specified.
• Discontinuous, non-Lipschitz, or undefined f values can invalidate convergence assumptions.
• Stiff systems may require implicit methods; the current honest label mentions stiffness but does not state that explicit Euler, RK4, and Dormand-Prince can fail or become impractical.
• Backward integration, interval endpoints not divisible by h, and rejected adaptive steps need explicit handling.
• Systems require componentwise absolute/relative tolerances or a clearly defined vector norm.

Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "method": "Euler",
    "f": "dy/dt = 1 metre/second",
    "initial_condition": {
      "t": 0,
      "y": 0
    },
    "interval": [
      0,
      1
    ],
    "step_size": 0.25,
    "units": {
      "t": "second",
      "y": "metre"
    }
  },
  "expected_outputs": {
    "trajectory": [
      {
        "t": 0,
        "y": 0
      },
      {
        "t": 0.25,
        "y": 0.25
      },
      {
        "t": 0.5,
        "y": 0.5
      },
      {
        "t": 0.75,
        "y": 0.75
      },
      {
        "t": 1,
        "y": 1
      }
    ],
    "final_y": 1
  },
  "working": "Use y_{n+1}=y_n+h f(t_n,y_n), with h=0.25 second and f=1 metre/second. Start y0=0. First step: y1=0+0.25*1=0.25 metre. Second: y2=0.25+0.25*1=0.50 metre. Third: y3=0.50+0.25*1=0.75 metre. Fourth: y4=0.75+0.25*1=1.00 metre. This is also the exact solution y=t for this constant-slope case. The zero initial value and interval boundary t=0 provide an edge case."
}

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json