Content deleted Content added
No edit summary |
Friedlemon (talk | contribs) Reverting edit(s) by 68.106.233.17 (talk) to rev. 963956996 by Inditer: Vandalism (RW 15) |
||
Line 15:
Initial value problems are extended to higher orders by treating the derivatives in the same way as an independent function, e.g. <math>y''(t)=f(t,y(t),y'(t))</math>.
== Existence and uniqueness of
For a large class of initial value problems, the existence and uniqueness of a solution can be illustrated through the use of a calculator.
The [[Picard–Lindelöf theorem]] guarantees a unique solution on some interval containing ''t''<sub>0</sub> if ƒ is continuous on a region containing ''t''<sub>0</sub> and ''y''<sub>0</sub> and satisfies the [[Lipschitz continuity|Lipschitz condition]] on the variable ''y''.
| |||