Math & Numbers

Runge-Kutta RK4 Solver (dy/dx = f(x, y))

Classical fourth-order Runge-Kutta for dy/dx = f(x, y): step table, k1–k4 stage details, final estimate, and optional exact-solution error column.

text· Text resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'http://127.0.0.1:3003/en/api/tools/runge-kutta-rk4-solver' \
  -H 'Content-Type: application/json' \
  -d '{"fxy":"y","x0":0,"y0":1,"xEnd":1,"steps":10,"exactY":"e^x","decimalPlaces":6}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST http://127.0.0.1:3003/en/api/tools/runge-kutta-rk4-solver

Parameters

Name	Type	Required	Description
fxy	text	Yes	Right-hand side in terms of x and y (functions: sin, cos, exp, ln, sqrt, …). Write products with , e.g. xy.
x0	number	Yes	—
y0	number	Yes	—
xEnd	number	Yes	Must be greater than x₀.
steps	number	Yes	h = (target x − x₀)/n. More steps → smaller error, O(h⁴) globally.

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-runge-kutta-rk4-solver": {
      "name": "runge-kutta-rk4-solver",
      "description": "Classical fourth-order Runge-Kutta for dy/dx = f(x, y): step table, k1–k4 stage details, final estimate, and optional exact-solution error column.",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=runge-kutta-rk4-solver",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "runge-kutta-rk4-solver",
    "arguments": {
  "fxy": "y",
  "x0": 0,
  "y0": 1,
  "xEnd": 1,
  "steps": 10,
  "exactY": "e^x",
  "decimalPlaces": 6
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

Browse tools Open tool