The following table summarizes the three methods.
| Scheme: | Truncation Error: | Stability requirements: |
| Crank-Nicolson | \( \mathcal{O}(\Delta x^2) \) and \( \mathcal{O}(\Delta t^2) \) | Stable for all \( \Delta t \) and \( \Delta x \). |
| Backward Euler | \( \mathcal{O}(\Delta x^2) \) and \( \mathcal{O}(\Delta t) \) | Stable for all \( \Delta t \) and \( \Delta x \). |
| Forward Euler | \( \mathcal{O}(\Delta x^2) \) and \( \mathcal{O}(\Delta t) \) | \( \Delta t\leq \frac{1}{2}\Delta x^2 \) |