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.
Original language | English |
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Pages (from-to) | 2260-2282 |
Number of pages | 23 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 51 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Aug 2013 |
Keywords
- nonlinear Volterra integral equations
- finite-time blow-up
- collocation methods
- adaptive stepsize
- convergence of numerical blow-up time