Superconvergent kernel functions approaches for the second kind Fredholm integral equations

X. Y. Li; B. Y. Wu

doi:10.1016/j.apnum.2021.05.004

Superconvergent kernel functions approaches for the second kind Fredholm integral equations

X. Y. Li
, B. Y. Wu^*

^*Corresponding author for this work

School of Mathematics

Changshu Institute of Technology
University of South Florida

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

20 Scopus citations

Abstract

By employing the kernel functions with the form of piecewise polynomials in the Sobolev reproducing kernel Hilbert spaces (RKHSs), a globally superconvergent numerical technique is proposed to solve the second kind linear integral equations of Fredholm type. This method has an order of global convergence O(h⁴) and O(h⁶) based on the kernel functions in the Sobolev RKHSs H¹ and H², respectively. Three linear Fredholm integral equations, one Volterra-Fredholm integral equation and one nonlinear Fredholm integral equation are numerically solved by the present approach to verify the superconvergence and effectiveness.

Original language	English
Pages (from-to)	202-210
Number of pages	9
Journal	Applied Numerical Mathematics
Volume	167
DOIs	https://doi.org/10.1016/j.apnum.2021.05.004
State	Published - Sep 2021

Keywords

Fredholm integral equations
Kernel functions
Superconvergence order

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10.1016/j.apnum.2021.05.004

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title = "Superconvergent kernel functions approaches for the second kind Fredholm integral equations",

abstract = "By employing the kernel functions with the form of piecewise polynomials in the Sobolev reproducing kernel Hilbert spaces (RKHSs), a globally superconvergent numerical technique is proposed to solve the second kind linear integral equations of Fredholm type. This method has an order of global convergence O(h4) and O(h6) based on the kernel functions in the Sobolev RKHSs H1 and H2, respectively. Three linear Fredholm integral equations, one Volterra-Fredholm integral equation and one nonlinear Fredholm integral equation are numerically solved by the present approach to verify the superconvergence and effectiveness.",

keywords = "Fredholm integral equations, Kernel functions, Superconvergence order",

author = "Li, \{X. Y.\} and Wu, \{B. Y.\}",

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

year = "2021",

month = sep,

doi = "10.1016/j.apnum.2021.05.004",

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AU - Li, X. Y.

AU - Wu, B. Y.

PY - 2021/9

Y1 - 2021/9

N2 - By employing the kernel functions with the form of piecewise polynomials in the Sobolev reproducing kernel Hilbert spaces (RKHSs), a globally superconvergent numerical technique is proposed to solve the second kind linear integral equations of Fredholm type. This method has an order of global convergence O(h4) and O(h6) based on the kernel functions in the Sobolev RKHSs H1 and H2, respectively. Three linear Fredholm integral equations, one Volterra-Fredholm integral equation and one nonlinear Fredholm integral equation are numerically solved by the present approach to verify the superconvergence and effectiveness.

AB - By employing the kernel functions with the form of piecewise polynomials in the Sobolev reproducing kernel Hilbert spaces (RKHSs), a globally superconvergent numerical technique is proposed to solve the second kind linear integral equations of Fredholm type. This method has an order of global convergence O(h4) and O(h6) based on the kernel functions in the Sobolev RKHSs H1 and H2, respectively. Three linear Fredholm integral equations, one Volterra-Fredholm integral equation and one nonlinear Fredholm integral equation are numerically solved by the present approach to verify the superconvergence and effectiveness.

KW - Fredholm integral equations

KW - Kernel functions

KW - Superconvergence order

UR - https://www.scopus.com/pages/publications/85105755461

U2 - 10.1016/j.apnum.2021.05.004

DO - 10.1016/j.apnum.2021.05.004

M3 - 文章

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SN - 0168-9274

VL - 167

SP - 202

EP - 210

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Superconvergent kernel functions approaches for the second kind Fredholm integral equations

Abstract

Keywords

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