An approximate solution of nonlinear hypersingular integral equations

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An approximate solution of nonlinear hypersingular integral equations. / Boykov, I.V.; Ventsel, E.S.; Roudnev, V.A.; Boykova, A.I.

In: Applied Numerical Mathematics, Vol. 86, 2014, p. 1-21.

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Author

Boykov, I.V. ; Ventsel, E.S. ; Roudnev, V.A. ; Boykova, A.I. / An approximate solution of nonlinear hypersingular integral equations. In: Applied Numerical Mathematics. 2014 ; Vol. 86. pp. 1-21.

BibTeX

@article{625f202d38b04ac484947d21908bb8c1,

title = "An approximate solution of nonlinear hypersingular integral equations",

abstract = "This paper describes numerical schemes based on spline-collocation method and their justifications for approximate solutions of linear and nonlinear hypersingular integral equations with singularities of the second kind. Collocations with continuous splines and piecewise constant functions are examined for solving linear hypersingular integral equations. Uniqueness of the solution has been proved. An error of approximation has been obtained for collocation with continuous spline in case a solution of equation has derivatives up to the second order. Collocation with piecewise constant functions are examined for nonlinear hypersingular equations. The convergence of the method has been justified. An estimate of error has been obtained. Illustrative examples demonstrate the accuracy and efficiency of the developed algorithms.",

author = "I.V. Boykov and E.S. Ventsel and V.A. Roudnev and A.I. Boykova",

year = "2014",

doi = "10.1016/j.apnum.2014.07.002",

language = "English",

volume = "86",

pages = "1--21",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - An approximate solution of nonlinear hypersingular integral equations

AU - Boykov, I.V.

AU - Ventsel, E.S.

AU - Roudnev, V.A.

AU - Boykova, A.I.

PY - 2014

Y1 - 2014

N2 - This paper describes numerical schemes based on spline-collocation method and their justifications for approximate solutions of linear and nonlinear hypersingular integral equations with singularities of the second kind. Collocations with continuous splines and piecewise constant functions are examined for solving linear hypersingular integral equations. Uniqueness of the solution has been proved. An error of approximation has been obtained for collocation with continuous spline in case a solution of equation has derivatives up to the second order. Collocation with piecewise constant functions are examined for nonlinear hypersingular equations. The convergence of the method has been justified. An estimate of error has been obtained. Illustrative examples demonstrate the accuracy and efficiency of the developed algorithms.

AB - This paper describes numerical schemes based on spline-collocation method and their justifications for approximate solutions of linear and nonlinear hypersingular integral equations with singularities of the second kind. Collocations with continuous splines and piecewise constant functions are examined for solving linear hypersingular integral equations. Uniqueness of the solution has been proved. An error of approximation has been obtained for collocation with continuous spline in case a solution of equation has derivatives up to the second order. Collocation with piecewise constant functions are examined for nonlinear hypersingular equations. The convergence of the method has been justified. An estimate of error has been obtained. Illustrative examples demonstrate the accuracy and efficiency of the developed algorithms.

U2 - 10.1016/j.apnum.2014.07.002

DO - 10.1016/j.apnum.2014.07.002

M3 - Article

VL - 86

SP - 1

EP - 21

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -

ID: 5724834