Analysis of Collocation Methods for Generalized Auto-Convolution Volterra Integral Equations

Ran Zhang; Hui Liang; Hermann Brunner

doi:10.1137/15M1019362

Analysis of Collocation Methods for Generalized Auto-Convolution Volterra Integral Equations

Ran Zhang
, Hui Liang
, Hermann Brunner

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

29 Citations (Scopus)

131 Downloads (Pure)

Abstract

We first study the existence, uniqueness, and regularity properties of solutions to a generalized version of the auto-convolution Volterra integral equation of the second kind. These results are then used to establish the optimal global and local (super) convergence properties of piecewise polynomial collocation solutions for such integral equations. The theoretical results are illustrated by extensive numerical examples.

Original language	English
Pages (from-to)	899-920
Number of pages	22
Journal	SIAM Journal on Numerical Analysis
Volume	54
Issue number	2
DOIs	https://doi.org/10.1137/15M1019362
Publication status	Published - 29 Mar 2016

User-Defined Keywords

Auto-convolution volterra integral equations
Collocation methods
Existence and regularity of solutions
Optimal order of convergence
Superconvergence

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10.1137/15M1019362

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title = "Analysis of Collocation Methods for Generalized Auto-Convolution Volterra Integral Equations",

abstract = "We first study the existence, uniqueness, and regularity properties of solutions to a generalized version of the auto-convolution Volterra integral equation of the second kind. These results are then used to establish the optimal global and local (super) convergence properties of piecewise polynomial collocation solutions for such integral equations. The theoretical results are illustrated by extensive numerical examples.",

keywords = "Auto-convolution volterra integral equations, Collocation methods, Existence and regularity of solutions, Optimal order of convergence, Superconvergence",

author = "Ran Zhang and Hui Liang and Hermann Brunner",

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N2 - We first study the existence, uniqueness, and regularity properties of solutions to a generalized version of the auto-convolution Volterra integral equation of the second kind. These results are then used to establish the optimal global and local (super) convergence properties of piecewise polynomial collocation solutions for such integral equations. The theoretical results are illustrated by extensive numerical examples.

AB - We first study the existence, uniqueness, and regularity properties of solutions to a generalized version of the auto-convolution Volterra integral equation of the second kind. These results are then used to establish the optimal global and local (super) convergence properties of piecewise polynomial collocation solutions for such integral equations. The theoretical results are illustrated by extensive numerical examples.

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KW - Optimal order of convergence

KW - Superconvergence

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Analysis of Collocation Methods for Generalized Auto-Convolution Volterra Integral Equations

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