Blow-up collocation solutions of some Volterra integral equations

Details Blow-up collocation solutions of some Volterra integral equations Blow-up collocation solutions of some Volterra integral equations

2011-12-20

arxiv.org/abs/1112.4658v1

Mathematics

Numerical Analysis

21 pages, 4 figures

Scientific paper

In this paper we use collocation methods for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, first we generalize the results on existence and uniqueness given in a previous paper in order to consider also non locally bounded kernels, which are present in many cases of blow-up problems. Next, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where the 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.

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