Compare numerical integration methods on classic ODEs
Euler's method (1st order) simply steps y_{n+1} = y_n + h·f(xₙ,yₙ). Midpoint method (2nd order) uses a half-step predictor. RK4 (4th order) averages four slope estimates — error scales as h⁴ vs Euler's h¹. Try increasing step size to see each method diverge.