ODE Solver: Euler vs RK4

Preset ODE (dy/dt = ...)

y'' + y = 0
Simple harmonic motion. Exact: y=cos(t). RK4 nearly perfect, Euler spirals outward.

Step size h 0.1 Time span 20 y₀ (initial value) dy₀/dt (initial velocity)

Exact / Reference

Euler (1st order)

Heun/RK2 (2nd order)

RK4 (4th order)