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THE FEUTEX TOOLKIT

Runge–Kutta Four-Stage Step

Combine four correctly evaluated Runge–Kutta stage slopes into one fourth-order solution step.

Math workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaNext = y+h*(k1+2*k2+2*k3+k4)/6; Increment = h*(k1+2*k2+2*k3+k4)/6; Euler Difference = h*((k1+2*k2+2*k3+k4)/6-k1)
Sources and model references

Worked example

Inputs

Current solution
1 value
Step size
0.1 time
First stage slope
1 value/time
Second stage slope
1.05 value/time
Third stage slope
1.0525 value/time
Fourth stage slope
1.10525 value/time

Expected results

Next
1.105170833 number
Increment
0.1051708333 number
Euler Difference
0.005170833333 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "y": 1,
  "h": 0.1,
  "k1": 1,
  "k2": 1.05,
  "k3": 1.0525,
  "k4": 1.10525
}

Accuracy and scope

Supply RK4 stage derivatives evaluated at their correct intermediate states; the workspace does not evaluate an arbitrary ODE. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.