620 B
620 B
| id | title | type | created | modified | tags |
|---|---|---|---|---|---|
| 20250911170650 | Lipschitz Continuous | permanent | 2025-09-11T21:06:50Z | 2025-09-16T16:32:37Z |
Lipschitz Continuous
Lipschitz continuous functions are a special case of
continuous functions. Lipschitz continuity means that a cone
can be created with slope less than some real number
K.
Fora a real valued function in one dimension, Lipschitz continuity is defined as:
| f(x_1) - f(x_2)| \leq K|x_1 - x_2|
Lipschitz continuity can be expanded to vector fields. From here, we can say that ODE trajectories do NOT intersect, and that every trajectory is unique.