CONTINUOUS PIECEWISE POLYNOMIAL COLLOCATION METHODS FOR GENERALIZED AUTO-CONVOLUTION VOLTERRA INTEGRAL EQUATIONS

Yuping Li; Hui Liang

doi:10.1216/jie.2023.35.41

CONTINUOUS PIECEWISE POLYNOMIAL COLLOCATION METHODS FOR GENERALIZED AUTO-CONVOLUTION VOLTERRA INTEGRAL EQUATIONS

Yuping Li^*
, Hui Liang

^*Corresponding author for this work

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

This paper fills a gap in the convergence analysis of collocation solutions in continuous piecewise polynomial space for generalized auto-convolution Volterra integral equations (AVIEs). The solvability of continuous collocation methods is discussed and the uniform boundedness of the collocation solution is provided by a discrete weighted exponential norm. The necessary and sufficient conditions for the optimal global and local (super-) convergence properties of continuous collocation solutions are obtained. Some numerical experiments are given to illustrate the theoretical results.

Original language	English
Pages (from-to)	41-59
Number of pages	19
Journal	Journal of Integral Equations and Applications
Volume	35
Issue number	1
DOIs	https://doi.org/10.1216/jie.2023.35.41
State	Published - 2023
Externally published	Yes

Keywords

Volterra integral equations
auto-convolution
continuous collocation methods
convergence
superconvergence

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10.1216/jie.2023.35.41

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title = "CONTINUOUS PIECEWISE POLYNOMIAL COLLOCATION METHODS FOR GENERALIZED AUTO-CONVOLUTION VOLTERRA INTEGRAL EQUATIONS",

abstract = "This paper fills a gap in the convergence analysis of collocation solutions in continuous piecewise polynomial space for generalized auto-convolution Volterra integral equations (AVIEs). The solvability of continuous collocation methods is discussed and the uniform boundedness of the collocation solution is provided by a discrete weighted exponential norm. The necessary and sufficient conditions for the optimal global and local (super-) convergence properties of continuous collocation solutions are obtained. Some numerical experiments are given to illustrate the theoretical results.",

keywords = "Volterra integral equations, auto-convolution, continuous collocation methods, convergence, superconvergence",

author = "Yuping Li and Hui Liang",

note = "Publisher Copyright: {\textcopyright} Rocky Mountain Mathematics Consortium",

year = "2023",

doi = "10.1216/jie.2023.35.41",

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T1 - CONTINUOUS PIECEWISE POLYNOMIAL COLLOCATION METHODS FOR GENERALIZED AUTO-CONVOLUTION VOLTERRA INTEGRAL EQUATIONS

AU - Li, Yuping

AU - Liang, Hui

N1 - Publisher Copyright: © Rocky Mountain Mathematics Consortium

PY - 2023

Y1 - 2023

N2 - This paper fills a gap in the convergence analysis of collocation solutions in continuous piecewise polynomial space for generalized auto-convolution Volterra integral equations (AVIEs). The solvability of continuous collocation methods is discussed and the uniform boundedness of the collocation solution is provided by a discrete weighted exponential norm. The necessary and sufficient conditions for the optimal global and local (super-) convergence properties of continuous collocation solutions are obtained. Some numerical experiments are given to illustrate the theoretical results.

AB - This paper fills a gap in the convergence analysis of collocation solutions in continuous piecewise polynomial space for generalized auto-convolution Volterra integral equations (AVIEs). The solvability of continuous collocation methods is discussed and the uniform boundedness of the collocation solution is provided by a discrete weighted exponential norm. The necessary and sufficient conditions for the optimal global and local (super-) convergence properties of continuous collocation solutions are obtained. Some numerical experiments are given to illustrate the theoretical results.

KW - Volterra integral equations

KW - auto-convolution

KW - continuous collocation methods

KW - convergence

KW - superconvergence

UR - https://www.scopus.com/pages/publications/85162172079

U2 - 10.1216/jie.2023.35.41

DO - 10.1216/jie.2023.35.41

M3 - 文章

AN - SCOPUS:85162172079

SN - 0897-3962

VL - 35

SP - 41

EP - 59

JO - Journal of Integral Equations and Applications

JF - Journal of Integral Equations and Applications

IS - 1

ER -

CONTINUOUS PIECEWISE POLYNOMIAL COLLOCATION METHODS FOR GENERALIZED AUTO-CONVOLUTION VOLTERRA INTEGRAL EQUATIONS

Abstract

Keywords

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