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 guarante...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 51; no. 4; pp. 2260 - 2282
Main Authors YANG, Z. W., BRUNNER, H.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects
Analytics
Applied mathematics
Approximation
Collocation
Convergence
Differential equations
Eulers method
Exact solutions
Integral equations
Mathematical analysis
Mathematical functions
Mathematical models
Mathematical problems
Odes
Research grants
Strategy
Textual collocation
Volterra integral equations
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Summary: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.
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ISSN:0036-1429
1095-7170
DOI:10.1137/12088238x