The method of Kantorovich majorants to nonlinear singular integral equation with shift

Amer, S. M.; Dardery, Samah M.

doi:10.1016/j.amc.2009.09.058

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…Eq. (26) has a unique solution (27) where the operator  is an integral operator which can be written in terms of powers of the operator  32, pp.378               , , , , , , , , , 3 2 1 0 3 2 1 0 2 3 2 1 0 3 (28) Such that the powers of  are also integrals operators. , , ; , , , , , , , 1 1 2 2 3 3 0 3 2 1 0 3…”

Section: Convergence Analysis and Mfmentioning

confidence: 99%

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Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

Hameed

Al-Saedi

2021

Baghdad Sci.J

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In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R 3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

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Section: Convergence Analysis and Mfmentioning

confidence: 99%

“…While Ezquerro and Hernandez-Veron in 26 applied the MF for concluding the approximate solution of some Hammerstein integral equations. The nonlinear singular integral equation in 27 has been solved via MF. In 28 , Argyros and Hilout provided the conditions of MF in a Banach space to study the local convergence of MNM.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

Hameed

Al-Saedi

2021

Baghdad Sci.J

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A Collocation Method for a Class of Nonlinear Singular Integral Equations with a Carleman Shift

Allan¹

2012

MCA

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The method of Kantorovich majorants to nonlinear singular integral equation with shift

Cited by 2 publications

References 17 publications

Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

A Collocation Method for a Class of Nonlinear Singular Integral Equations with a Carleman Shift

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