On the notion of the finite part of divergent integrals in integral equations

DOI10.1023/A:1021700706820zbMath1040.65109OpenAlexW174227930MaRDI QIDQ1873524

I. K. Lifanov, Gennadi Vainikko

Publication date: 25 May 2003

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1021700706820

zbMATH Keywords

singular integral equationssingular integralsCauchy principal value integralhypersingular integralsHadamard finite part integraldivergent integrals

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integral equations with kernels of Cauchy type (45E05)

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Quadrature rules for finite element approximations of 1D nonlocal problems ⋮ Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals ⋮ Superconvergence of Newton-Cotes rule for computing hypersingular integral on a circle ⋮ Nodal-type collocation methods for hypersingular integral equations and nonlocal diffusion problems ⋮ Collocation method for one dimensional nonlocal diffusion equations ⋮ A multiscale method for nonlocal mechanics and diffusion and for the approximation of discontinuous functions ⋮ Nodal-Type Newton-Cotes Rules for Fractional Hypersingular Integrals ⋮ Superconvergence of Hermite rule for hypersingular integrals on interval

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