The exact solution and stability analysis for integral equation of third or first kind with singular kernel

Wei Jiang; Minggen Cui

doi:10.1016/j.amc.2008.03.005

The exact solution and stability analysis for integral equation of third or first kind with singular kernel

Wei Jiang
, Minggen Cui^*

^*Corresponding author for this work

Harbin Institute of Technology Weihai

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

13 Scopus citations

Abstract

In this paper, we give representation of exact solution for integral equation of third or first kind with singular kernel by the form of series in the reproducing kernel space. The n-term approximate to the exact solution is obtained by truncating the series and the error is monotone decreasing with increasing item of the n-term approximate solution. The solution is stable in the reproducing kernel space. Some numerical examples are studied to demonstrate the accuracy of the present method.

Original language	English
Pages (from-to)	666-674
Number of pages	9
Journal	Applied Mathematics and Computation
Volume	202
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2008.03.005
State	Published - 15 Aug 2008
Externally published	Yes

Keywords

Exact solution
Integral equations of third or first kind
Reproducing kernel space
Singular kernel
Stable

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10.1016/j.amc.2008.03.005

Cite this

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abstract = "In this paper, we give representation of exact solution for integral equation of third or first kind with singular kernel by the form of series in the reproducing kernel space. The n-term approximate to the exact solution is obtained by truncating the series and the error is monotone decreasing with increasing item of the n-term approximate solution. The solution is stable in the reproducing kernel space. Some numerical examples are studied to demonstrate the accuracy of the present method.",

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author = "Wei Jiang and Minggen Cui",

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AU - Jiang, Wei

AU - Cui, Minggen

PY - 2008/8/15

Y1 - 2008/8/15

N2 - In this paper, we give representation of exact solution for integral equation of third or first kind with singular kernel by the form of series in the reproducing kernel space. The n-term approximate to the exact solution is obtained by truncating the series and the error is monotone decreasing with increasing item of the n-term approximate solution. The solution is stable in the reproducing kernel space. Some numerical examples are studied to demonstrate the accuracy of the present method.

AB - In this paper, we give representation of exact solution for integral equation of third or first kind with singular kernel by the form of series in the reproducing kernel space. The n-term approximate to the exact solution is obtained by truncating the series and the error is monotone decreasing with increasing item of the n-term approximate solution. The solution is stable in the reproducing kernel space. Some numerical examples are studied to demonstrate the accuracy of the present method.

KW - Exact solution

KW - Integral equations of third or first kind

KW - Reproducing kernel space

KW - Singular kernel

KW - Stable

UR - https://www.scopus.com/pages/publications/48049092251

U2 - 10.1016/j.amc.2008.03.005

DO - 10.1016/j.amc.2008.03.005

M3 - 文章

AN - SCOPUS:48049092251

SN - 0096-3003

VL - 202

SP - 666

EP - 674

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

The exact solution and stability analysis for integral equation of third or first kind with singular kernel

Abstract

Keywords

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