Euler’s Method

Solving by taking small steps

An interactive lesson with 6 steps, about 5 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: $y_{n+1} = y_n + h\,F(x_n, y_n)$.
• Smaller steps are more accurate (the error shrinks roughly in proportion to h).
• On $y' = y$ it gives $(1 + 1/n)^n \to e$.

Steps

1. When formulas run out
2. Estimating e
3. Two steps by hand
4. Halving the step
5. Decay by Euler
6. A new equation