Calculus & Numerical Methods
Runge-Kutta 4 (ODE)
Solve y' = f(x, y) with the classic RK4 method.
Formula
Formula
yn+1 = yn + h6(k1+2k2+2k3+k4)
Variables
| Symbol | Definition | Type & range | Units | Role |
|---|---|---|---|---|
| f | derivative function | expression / text | x, y | input |
| x₀, y₀ | initial condition | real number (ℝ) | — | input |
| x | target | real number (ℝ) | — | input |
Try it yourself
Interactive calculator
Worked examples
Example 1
Givenf(x, y) = x + y, x₀ = 0, y₀ = 1, target x = 1, steps = 100
Result3.436563656
Example 2
Givenf(x, y) = y, x₀ = 0, y₀ = 1, target x = 1, steps = 100
Result2.718281828