On the application of the newton-kantorovich method to nonlinear integral equations of uryson type

Appell, Jürgen; Pascale, Espedito De; Zabrejko, Petr P.

doi:10.1080/01630569108816428

Cited by 34 publications

(31 citation statements)

References 3 publications

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“…Then sequence {x n } generated by iterative method (2) is well defined, remains in U (x * , r * ) for all n ≥ 0, and converges to x * provided that…”

Section: Local Convergence Of Methods (2)mentioning

confidence: 98%

Approximating Solutions of Equations Using Two‐Point Newton Methods

Argyros

2004

Appl Numer Analy & Comput

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We provide a local as well as a semilocal convergence analysis for two-point Newton methods under very general conditions. Our equation contains a Fréchet differentiable operator F and another operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton methods to a locally unique solution of equation F (x) + G (x) = 0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results [17]. In the local case a larger radius of convergence is obtained [21]

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“…Then sequence {x n } generated by iterative method (2) is well defined, remains in U (x * , r * ) for all n ≥ 0, and converges to x * provided that…”

Section: Local Convergence Of Methods (2)mentioning

confidence: 98%

Approximating Solutions of Equations Using Two‐Point Newton Methods

Argyros

2004

Appl Numer Analy & Comput

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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%

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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“…2 Faculty of Education, Cumhuriyet University, Sivas, 58140, Turkey. 3 Faculty of Science, Cumhuriyet University, Sivas, 58140, Turkey.…”

Section: Competing Interestsmentioning

confidence: 99%

Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions

Alias

Hüseyin

2016

J Inequal Appl

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In this paper the control system is considered described by a Urysohn type integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector. The functions from the space L 2 ([t 0 , θ ]; R m ) satisfying a quadratic integral constraint are chosen as admissible control functions. The set of trajectories generated by all admissible control functions is studied. The boundedness, closedness, precompactness, and hence the compactness of the set of trajectories in the space of continuous functions is proved. MSC: 45G15; 93C10

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On the application of the newton-kantorovich method to nonlinear integral equations of uryson type

Cited by 34 publications

References 3 publications

Approximating Solutions of Equations Using Two‐Point Newton Methods

Approximating Solutions of Equations Using Two‐Point Newton Methods

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

Compactness of the set of trajectories of the control system described by a Urysohn type integral equation with quadratic integral constraints on the control functions

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