Multistep collocation approximations to solutions of first-kind Volterra integral equations

Tingting Zhang; Hui Liang

doi:10.1016/j.apnum.2018.04.005

Multistep collocation approximations to solutions of first-kind Volterra integral equations

Tingting Zhang
, Hui Liang^*

^*Corresponding author for this work

Heilongjiang University
National Key Laboratory of Complex System Control and Intelligent Agent Cooperation

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

17 Scopus citations

Abstract

The multistep collocation method is applied to Volterra integral equations of the first kind. The existence and uniqueness of the multistep collocation solution are proved. Then the convergence condition of the multistep collocation method is analyzed and the corresponding convergence order is described. In particular, for c_m=1, the convergence conditions, which can be easily implemented, are given for two-step and three-step collocation methods. Numerical experiments illustrate the theoretical analysis.

Original language	English
Pages (from-to)	171-183
Number of pages	13
Journal	Applied Numerical Mathematics
Volume	130
DOIs	https://doi.org/10.1016/j.apnum.2018.04.005
State	Published - Aug 2018
Externally published	Yes

Keywords

Convergence
First kind
Multistep collocation methods
Volterra integral equations

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10.1016/j.apnum.2018.04.005

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title = "Multistep collocation approximations to solutions of first-kind Volterra integral equations",

abstract = "The multistep collocation method is applied to Volterra integral equations of the first kind. The existence and uniqueness of the multistep collocation solution are proved. Then the convergence condition of the multistep collocation method is analyzed and the corresponding convergence order is described. In particular, for cm=1, the convergence conditions, which can be easily implemented, are given for two-step and three-step collocation methods. Numerical experiments illustrate the theoretical analysis.",

keywords = "Convergence, First kind, Multistep collocation methods, Volterra integral equations",

author = "Tingting Zhang and Hui Liang",

note = "Publisher Copyright: {\textcopyright} 2018 IMACS",

year = "2018",

month = aug,

doi = "10.1016/j.apnum.2018.04.005",

language = "英语",

volume = "130",

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AU - Zhang, Tingting

AU - Liang, Hui

PY - 2018/8

Y1 - 2018/8

N2 - The multistep collocation method is applied to Volterra integral equations of the first kind. The existence and uniqueness of the multistep collocation solution are proved. Then the convergence condition of the multistep collocation method is analyzed and the corresponding convergence order is described. In particular, for cm=1, the convergence conditions, which can be easily implemented, are given for two-step and three-step collocation methods. Numerical experiments illustrate the theoretical analysis.

AB - The multistep collocation method is applied to Volterra integral equations of the first kind. The existence and uniqueness of the multistep collocation solution are proved. Then the convergence condition of the multistep collocation method is analyzed and the corresponding convergence order is described. In particular, for cm=1, the convergence conditions, which can be easily implemented, are given for two-step and three-step collocation methods. Numerical experiments illustrate the theoretical analysis.

KW - Convergence

KW - First kind

KW - Multistep collocation methods

KW - Volterra integral equations

UR - https://www.scopus.com/pages/publications/85045874188

U2 - 10.1016/j.apnum.2018.04.005

DO - 10.1016/j.apnum.2018.04.005

M3 - 文章

AN - SCOPUS:85045874188

SN - 0168-9274

VL - 130

SP - 171

EP - 183

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Multistep collocation approximations to solutions of first-kind Volterra integral equations

Abstract

Keywords

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