Super-convergence analysis of collocation methods for linear and nonlinear third-kind Volterra integral equations with non-compact operators

Huiming Song; Zhanwen Yang; Yu Xiao

doi:10.1016/j.amc.2021.126562

Super-convergence analysis of collocation methods for linear and nonlinear third-kind Volterra integral equations with non-compact operators

Huiming Song
, Zhanwen Yang
, Yu Xiao^*

^*Corresponding author for this work

School of Mathematics

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

5 Scopus citations

Abstract

This paper concerns iterated collocation methods for linear and nonlinear Volterra integral equations (VIEs) of the third kind with noncompact operators. The optimal global and local super-convergence orders are determined under a new mesh. Finally, some numerical examples are provided to verify the convergence results.

Original language	English
Article number	126562
Journal	Applied Mathematics and Computation
Volume	412
DOIs	https://doi.org/10.1016/j.amc.2021.126562
State	Published - 1 Jan 2022

Keywords

Iterated collocation methods
Noncompact operator
Super-convergence order
Volterra integral equations of third kind

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10.1016/j.amc.2021.126562

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title = "Super-convergence analysis of collocation methods for linear and nonlinear third-kind Volterra integral equations with non-compact operators",

abstract = "This paper concerns iterated collocation methods for linear and nonlinear Volterra integral equations (VIEs) of the third kind with noncompact operators. The optimal global and local super-convergence orders are determined under a new mesh. Finally, some numerical examples are provided to verify the convergence results.",

keywords = "Iterated collocation methods, Noncompact operator, Super-convergence order, Volterra integral equations of third kind",

author = "Huiming Song and Zhanwen Yang and Yu Xiao",

note = "Publisher Copyright: {\textcopyright} 2021",

year = "2022",

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AU - Song, Huiming

AU - Yang, Zhanwen

AU - Xiao, Yu

PY - 2022/1/1

Y1 - 2022/1/1

N2 - This paper concerns iterated collocation methods for linear and nonlinear Volterra integral equations (VIEs) of the third kind with noncompact operators. The optimal global and local super-convergence orders are determined under a new mesh. Finally, some numerical examples are provided to verify the convergence results.

AB - This paper concerns iterated collocation methods for linear and nonlinear Volterra integral equations (VIEs) of the third kind with noncompact operators. The optimal global and local super-convergence orders are determined under a new mesh. Finally, some numerical examples are provided to verify the convergence results.

KW - Iterated collocation methods

KW - Noncompact operator

KW - Super-convergence order

KW - Volterra integral equations of third kind

UR - https://www.scopus.com/pages/publications/85112666725

U2 - 10.1016/j.amc.2021.126562

DO - 10.1016/j.amc.2021.126562

M3 - 文章

AN - SCOPUS:85112666725

SN - 0096-3003

VL - 412

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 126562

ER -

Super-convergence analysis of collocation methods for linear and nonlinear third-kind Volterra integral equations with non-compact operators

Abstract

Keywords

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