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.
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Quick start
Call this tool from your code in three languages.
cURL
curl -X POST 'https://api.elysiatools.com/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 https://api.elysiatools.com/en/api/tools/runge-kutta-rk4-solverParameters
| 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. x*y. |
| 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": "https://api.elysiatools.com/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]