A new method for solving Hilbert type singular integral equations

Zhong Chen; Yongfang Zhou

doi:10.1016/j.amc.2011.05.078

A new method for solving Hilbert type singular integral equations

Zhong Chen^*
, Yongfang Zhou

^*Corresponding author for this work

School of Science

Harbin Institute of Technology
Heilongjiang University of Science and Technology

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

8 Scopus citations

Abstract

A simple method for solving Hilbert type singular integral equations is proposed. Using the reproducing kernel as the basis of W21[0,2π], the singularity of the considered equation is removed skillfully. Since the problem is discussed in space W21[0,2π], which only require the absolute continuity of the considered function, our method is effective not only for smooth solutions, but also for non-smooth solutions. The final numerical examples show the efficiency of the proposed method.

Original language	English
Pages (from-to)	406-412
Number of pages	7
Journal	Applied Mathematics and Computation
Volume	218
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2011.05.078
State	Published - 15 Sep 2011

Keywords

Approximate solution
Hilbert type singular integral equations
Reproducing kernel space

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10.1016/j.amc.2011.05.078

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abstract = "A simple method for solving Hilbert type singular integral equations is proposed. Using the reproducing kernel as the basis of W21[0,2π], the singularity of the considered equation is removed skillfully. Since the problem is discussed in space W21[0,2π], which only require the absolute continuity of the considered function, our method is effective not only for smooth solutions, but also for non-smooth solutions. The final numerical examples show the efficiency of the proposed method.",

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AB - A simple method for solving Hilbert type singular integral equations is proposed. Using the reproducing kernel as the basis of W21[0,2π], the singularity of the considered equation is removed skillfully. Since the problem is discussed in space W21[0,2π], which only require the absolute continuity of the considered function, our method is effective not only for smooth solutions, but also for non-smooth solutions. The final numerical examples show the efficiency of the proposed method.

KW - Approximate solution

KW - Hilbert type singular integral equations

KW - Reproducing kernel space

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ER -

A new method for solving Hilbert type singular integral equations

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Keywords

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