Solving nonlinear integral equations in the Urysohn form by Newton–Kantorovich–quadrature method

Saberi‐Nadjafi, Jafar; Heidari, Mahdi

doi:10.1016/j.camwa.2010.07.046

Cited by 34 publications

(48 citation statements)

References 2 publications

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“…As x 0 (s) = sin(πs) is a reasonable choice as a starting point for Newton's method, as we can see in [12][13][14], the last inequality holds, since 1 0 sin(πt) cos(πt)x 0 (t) 2 dt = 0, and condition (6) is omitted.…”

Section: Applicationmentioning

confidence: 99%

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On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique

Ezquerro¹,

Hernández‐Verón²

2017

Algorithms

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Abstract:The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton's method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for these equations. Finally, we illustrate the above with two particular Fredholm integral equations.Keywords: Fredholm integral equation; Newton's method; convergence; Kantorovich's technique; domain of existence of a solution; domain of uniqueness of a solution.

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Section: Applicationmentioning

confidence: 99%

“…In [13], the authors present an adapted modification to the Newton-Kantorovich method. Finally, in [14], the Newton-Kantorovich method and quadrature methods are combined to develop a new method for solving Equation (1).…”

Section: Introductionmentioning

confidence: 99%

On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique

Ezquerro¹,

Hernández‐Verón²

2017

Algorithms

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“…The following iteration method is used to solve the following sequence of linear integral equations instead of a nonlinear integral equation. For further information on the Newton-Kantorovich method, see Saberi-Nadjafi and Heidari 35 , Appell et al 50 and Polyanin and Manzhirov 51 .…”

Section: Basic Nkq Equationsmentioning

confidence: 99%

“…In NKQ method which is used in this paper, Equations 11-13 are combined by Saberi-Najafi and Heidari 35 to solve the nonlinear integral equations.…”

Section: Basic Nkq Equationsmentioning

confidence: 99%

“…The aim of this work is to achieve a semi-analytical approach for the non-linear model of laminated plates with arbitrary boundary conditions for general out-of-plane loadings. A Newton-Kantorovich-Quadrature (NKQ) method was proposed recently, by Saberi-Najafi and Heidari 35 , for solving nonlinear integral equations in the Urysohn form. This method is expanded and used in this paper to present a semi-analytical model for laminated composite plates.…”

Section: Introductionmentioning

confidence: 99%

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A semi-analytical model for deflection analysis of laminated plates with the Newton-Kantorovich-Quadrature method

et al. 2012

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A semi-analytical approach for analysis of laminated plates with general boundary conditions under a general distribution of loads is developed. The non-linear equations are solved by the NewtonKantorovich-Quadrature (NKQ) method which is a combination of well-known Newton-Kantorovich method and the Quadrature method. This method attempts to solve a sequence of linear integral equations. The convergence of the proposed method is compared with other semi-analytical methods. The validation of the method is explored through various numerical examples and the results compared with finite element method (FEM) and experimental tests. Good agreement between the NKQ model, FEM and experimental results are shown to validate the model.

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A numerical technique for solving Volterra-Fredholm integral equations using Chebyshev spectral method

Khidir

2022

Ricerche mat

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Solving nonlinear integral equations in the Urysohn form by Newton–Kantorovich–quadrature method

Cited by 34 publications

References 2 publications

On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique

On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique

A semi-analytical model for deflection analysis of laminated plates with the Newton-Kantorovich-Quadrature method

A numerical technique for solving Volterra-Fredholm integral equations using Chebyshev spectral method

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