API & MCP

Everything a person can do on ODE Solver (Runge–Kutta), a program or AI agent can do with the same inputs and get the identical result.

HTTP API

POST https://prooflineodesolver.usefulweb.app/api/v1/calculate – run ODE Solver (Runge–Kutta)
GET https://prooflineodesolver.usefulweb.app/api/v1/tool – inputs, output schema, examples
OpenAPI 3.1: /openapi.json · /openapi.yaml
Errors: application/problem+json; 422 includes per-field errors.

ODE Solver (Runge–Kutta)

Type a differential equation or a system such as x′ = v, v′ = −x with initial values and parameters, and get the solution table, a plot of every variable, a phase portrait for two variables and a CSV download. Uses the adaptive Dormand–Prince RK45 method with error control or classical fixed-step RK4, and reports steps and function evaluations. Part of the Proofline math notebook.

Inputs of ODE Solver (Runge–Kutta)
Field	Type	Default	Description
`equations` (required)	textarea	—	Equations. One equation per line: y' = expression or dy/dt = expression. Right-hand sides may use the independent variable, every state variable and the parameters. Use + − * / ^, implicit products (2x), sin, cos, tan, exp, ln (natural log), log (base 10), sqrt, abs, pi and e. Angles are in radians.
`initial` (required)	text	—	Initial values. One value per state variable at the start time, e.g. x = 1, v = 0.
`parameters`	text	—	Parameters. Optional constants used in the equations, e.g. a = 1.1, b = 0.4.
`variable`	text	"t"	Independent variable
`tStart`	number	0	Start time
`tEnd`	number	10	End time
`method`	select (rk45, rk4)	"rk45"	Method
`tolerance`	number	1e-8	Tolerance (RK45). Relative error allowed per step; the absolute tolerance is 1/100 of it.
`step`	number	—	Step size (RK4). Default: 1/1000 of the interval.
`outputPoints`	integer	101	Output points. Equally spaced times in the table, plot and CSV (start and end included).

Example request

Exponential decay y′ = −k·y

curl -X POST https://prooflineodesolver.usefulweb.app/api/v1/calculate -H 'content-type: application/json' -d '{"equations":"y' = -k*y","initial":"y = 1","parameters":"k = 0.5","tEnd":10}'

Every result contains

inputs (normalised, defaults applied), summary, result (validated against the published schema), units, assumptions, sources, warnings, computedAt and links.

MCP (Model Context Protocol)

Streamable HTTP endpoint: https://prooflineodesolver.usefulweb.app/mcp – protocol revisions 2026-07-28 (stateless) and 2025-11-25 / 2025-06-18 / 2025-03-26 (initialize handshake).
Tools: proofline_ode_solver
Local stdio connector: node src/mcp-stdio.ts --tool=proofline-ode-solver

{
  "mcpServers": {
    "proofline-ode-solver": { "type": "http", "url": "https://prooflineodesolver.usefulweb.app/mcp" }
  }
}