Department of Mathematics
Blow-up behavior of collocation solutions to hammerstein-type volterra integral equations
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.
Adaptive stepsize, Collocation methods, Convergence of numerical blow-up time, Finite-time blow-up, Nonlinear Volterra integral equations
Source Publication Title
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics
Link to Publisher's Edition
Yang, Z. W., and H. Brunner. "Blow-up behavior of collocation solutions to hammerstein-type volterra integral equations." SIAM Journal on Numerical Analysis 51.4 (2013): 2260-2282.