Hokkaido Mathematical Journal

Approximations of hypersingular integral equations by the quadrature method

E.G. LADOPOULOS and V.A. ZISIS

Full-text: Open access

Abstract

A numerical method is proposed and investigated for the hypersingular integral equations defined in Banach spaces. The hypersingular integral equations belong to a wider class of singular integral equations having much more stronger singularities. The proposed approximation method is an extension beyond the quadrature method.Moreover an error estimates theory is introduced for the hypersingular integral equations by proving the proper theorem. Finally, the inequalities valid between the exact solutions of the hypersingular integral equations and the corresponding approximate solutions, are proposed and proved.

Article information

Source
Hokkaido Math. J., Volume 35, Number 2 (2006), 457-469.

Dates
First available in Project Euclid: 29 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1285766365

Digital Object Identifier
doi:10.14492/hokmj/1285766365

Mathematical Reviews number (MathSciNet)
MR2254660

Zentralblatt MATH identifier
1117.57028

Subjects
Primary: 65R20: Integral equations
Secondary: 65L10: Boundary value problems

Keywords
hypersingular integral equations singularity quadrature method error estimate,Banach spaces

Citation

LADOPOULOS, E.G.; ZISIS, V.A. Approximations of hypersingular integral equations by the quadrature method. Hokkaido Math. J. 35 (2006), no. 2, 457--469. doi:10.14492/hokmj/1285766365. https://projecteuclid.org/euclid.hokmj/1285766365


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