Well-posedness

In addition to existence and uniqueness, we will want to know something about the stability of solutions of the IVP. In particular, we will usually be interested in the sensitivity of the solution to small changes in the data. Perturbations arise naturally in numerical computation due to discretization and round off errors. A formal study of sensitivity would lead us to the following notion of a well posed problem.

Definition: The IVP

(1.7)

is well-posed if there exist positive constants K and such that, for any , the perturbed IVP

	(1.8)

satisfies

(1.9)

whenever for .

Remark: By well-posedness, we mean that small perturbations in the stated problem will lead to small changes in the solutions.