Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Uniform error estimates of Galerkin methods for monotone Abel-Volterra integral equations on the half-line

Author: P. P. B. Eggermont
Journal: Math. Comp. 53 (1989), 157-189
MSC: Primary 65R20; Secondary 45D05, 47H17
MathSciNet review: 969485
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider Galerkin methods for monotone Abel-Volterra integral equations of the second kind on the half-line. The $ {L^2}$ theory follows from Kolodner's theory of monotone Hammerstein, equations. We derive the $ {L^\infty }$ theory from the $ {L^2}$ theory by relating the $ {L^2}$- and $ {L^\infty }$-spectra of operators of the form $ x \to b \ast (ax)$ to one another. Here $ \ast $ denotes convolution, and $ b \in {L^1}$ and $ a \in {L^\infty }$. As an extra condition we need $ b(t) = O({t^{ - \alpha - 1}})$, with $ \alpha > 0$. We also prove the discrete analogue. In particular, we verify that the Galerkin matrix satisfies the "discrete" conditions.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65R20, 45D05, 47H17

Retrieve articles in all journals with MSC: 65R20, 45D05, 47H17

Additional Information

PII: S 0025-5718(1989)0969485-X
Article copyright: © Copyright 1989 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia