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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Blow-up behavior of collocation solutions to hammerstein-type volterra integral equations

Language

English

Abstract

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein- type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis. © 2013 Society for Industrial and Applied Mathematics.

Keywords

Adaptive stepsize, Collocation methods, Convergence of numerical blow-up time, Finite-time blow-up, Nonlinear Volterra integral equations

Publication Date

2013

Source Publication Title

SIAM Journal on Numerical Analysis

Volume

51

Issue

4

Start Page

2260

End Page

2282

Publisher

Society for Industrial and Applied Mathematics

ISSN (print)

00361429

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