The stability condition for the Forward Euler method can be expressed mathematically as:[^1]
|1 + hλ| <= 1,
where h is the step size and λ is the eigenvalue of the problem being solved.[^1] The above equation states that the magnitude of the solution to the recurrence relation produced by the Forward Euler method will remain bounded if and only if the value of |1 + hλ| is less than or equal to 1.[^1] In other words, the stability region for the Forward Euler method is a circle with radius 1 centered at the origin in the complex plane, and any eigenvalue with a magnitude greater than 1/h will cause the solution to become unstable.[^1]
- StabilityRegionsEuler[^1]