Hokkaido Mathematical Journal
- Hokkaido Math. J.
- Volume 35, Number 2 (2006), 457-469.
Approximations of hypersingular integral equations by the quadrature method
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.
Hokkaido Math. J., Volume 35, Number 2 (2006), 457-469.
First available in Project Euclid: 29 September 2010
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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