On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation [PDF]
Abstract and Applied Analysis, 2015 We develop the Newton-Kantorovich method to solve the system of 2×2 nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval.
Hameed Husam Hameed +3 more
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Uniformly convergent computational method for singularly perturbed unsteady burger-huxley equation [PDF]
MethodsX, 2022 This paper deals with the numerical treatment of a singularly perturbed unsteady non-linear Burger-Huxley problem. Due to the simultaneous presence of a singular perturbation parameter and non-linearity in the problem applying classical numerical methods
Imiru Takele Daba, Gemechis File Duressa
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New and Generalized Convergence Conditions for the Newton-Kantorovich Method [PDF]
Journal of Applied Analysis, 2003 For a nonlinear operator equation on a Banach space a semilocal convergence theorem for Newton's method is proved using a majorant principle. This is shown to provide some weakening of the usual results based on Lipschitz conditions. Few connections are made to the literature on other related work involving majorization techniques.
I K Argyros
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A modification of the classic conditions of Newton–Kantorovich for Newton’s method
Mathematical and Computer Modelling, 2013 Abstract We study the semilocal convergence of Newton’s method in Banach spaces under a modification of the classic conditions of Kantorovich, which leads to a generalization of Kantorovich’s theory. We illustrate this study with two Hammerstein integral equations of the second kind, where the classic conditions of Kantorovich cannot be applied, but ...
M A Hernández, J A Ezquerro
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A hybrid computational scheme for singularly perturbed Burgers’-Huxley equation [PDF]
MethodsXThis paper aims to construct and analyze a hybrid computational method for the nonlinear singularly perturbed Burgers’-Huxley equation. The presence of the perturbation parameter and non-linearity in the considered problem makes it difficult to solve the
Imiru Takele Daba, Genanew Gofe Gonfa
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Approximate solution of the system of nonlinear integral equation by Newton–Kantorovich method [PDF]
Applied Mathematics and Computation, 2010 The authors consider a system of nonlinear Volterra integral equations, which is solved by successive approximations. A result on the convergence rate of the approximate solution is presented, and some numerical examples are discussed.
Anvarjon Ahmedov, N M A Nik Long
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Estimates of majorizing sequences in the Newton–Kantorovich method: A further improvement
Journal of Mathematical Analysis and Applications, 2006 Majorizing sequences, a widespread tool to estimate the convergence of the Newton-Kantorovich method, are studied for operators with Hölder continuous derivatives. The authors improve their previous estimate on the convergence of a proper majorizing sequence.
Filomena Cianciaruso +1 more
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Solving nonlinear integral equations in the Urysohn form by Newton–Kantorovich–quadrature method
Computers and Mathematics With Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jafar Saberi-Nadjafi, Mahdi Heidari
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Newton-Kantorovich Method for Solving One of the Non-Linear Sturm-Liouville Problems
مجلة بغداد للعلوم, 2023 Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich method is applied in this work to one of the non ...
Hussien A. H. Abugirda +2 more
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NONLINEAR STRUCTURAL ANALYSIS BASED ON THE MODIFIED SEQUENTIAL LOAD METHOD
International Journal for Computational Civil and Structural Engineering, 2021 The article discusses ways to improve the accuracy of solving problems of nonlinear structural mechanics. It is shown that the combination of the method of sequential loading and the Newton-Kantorovich method can improve the accuracy of the solution and ...
Vladilen Petrov
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