DSM of Newton type for solving operator equations F(u) = f with minimal smoothness assumptions on F Online publication date: Sun, 04-Jul-2010
by N.S. Hoang, A.G. Ramm
International Journal of Computing Science and Mathematics (IJCSM), Vol. 3, No. 1/2, 2010
Abstract: This paper is a review of the authors' results on the Dynamical Systems Method (DSM) for solving operator equation (*) F(u) = f. It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F. It is assumed that F is continuously Frechet differentiable, but no smoothness assumptions on F′(u) are imposed. The DSM for solving equation (*) is developed. Under weak assumptions global existence of the solution u(t) is proved, the existence of u(∞) is established, and the relation F(u(∞)) = f is obtained. The DSM is developed for a stable solution of equation (*) when noisy data fδ are given, ''f − fδ'' ≤ δ.
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Computing Science and Mathematics (IJCSM):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.
If you still need assistance, please email subs@inderscience.com