Hokkaido Mathematical Journal

LADOPOULOS E.G., ZISIS V.A.,

Approximations of hypersingular integral equations by the quadrature method.

Hokkaido Mathematical Journal, 35 (2006) pp.457-469

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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.

MSC(Primary)65R20
MSC(Secondary)65L10
Uncontrolled Keywordshypersingular integral equations, singularity, quadrature method, error estimate,Banach spaces