# ODELC3

From Example Problems

For the first-order system , show that the right-hand side satisfies a Lipschitz condition in the domain for , where and are arbitrary but finite numbers. Deduce that the IVP and has a unique solution for and obtain an estimate for . By allowing and to be as large as possible, attempt to improve your estimate of .

The Lipschitz constant is .

If then

The magnitude of gives an upper bound:

Let

Pick so that .

Improve the estimate for by allowing and to be as large as possible.

Maximize .

The derivative is .

Just set the numerator equal to 0.

Now let so that

Main Page : Ordinary Differential Equations : Lipshitz Conditions