Source: https://guthlabs.ai/docs/instruments/ode-solver-euler-rk4-rk45/implementation/

instrument implementation / implementation-contract

# ODE Solver (Euler / RK4 / RK45) implementation

A source-bound implementation contract for ODE Solver (Euler / RK4 / RK45); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/ode-solver-euler-rk4-rk45/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/ode-solver-euler-rk4-rk45/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/ode-solver-euler-rk4-rk45/qualification/>)

## 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`