English

Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations

Numerical Analysis 2015-02-18 v2 Analysis of PDEs

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