Stepping Through Time

Solving differential equations numerically

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Euler’s method: $y_{n+1} = y_n + h f(t_n, y_n)$; error $\propto h$.
• The midpoint method samples the slope halfway; error $\propto h^2$.
• Higher-order methods like RK4 reach high accuracy with far fewer steps.

Steps

1. Follow the slope
2. Two Euler steps
3. How many steps?
4. Euler spirals out
5. Orders of accuracy
6. Fourth order
7. A tenth of a percent