Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations
Abstract
In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.
Keywords
Cite
@article{arxiv.1112.4658,
title = {Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations},
author = {Vicente J. Bolós and Rafael Benítez},
journal= {arXiv preprint arXiv:1112.4658},
year = {2015}
}
Comments
22 pages, 5 figures. New version: We have made some notation changes in order to make emphasis in the fact that we use variable stepsizes, for preventing misunderstandings (a referee misunderstood it). arXiv admin note: text overlap with arXiv:1112.4649