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
doaj +3 more sources
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
Daba IT, Duressa GF.
europepmc +2 more sources
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 ...
J A Ezquerro +2 more
exaly +2 more sources
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
Daba IT, Gonfa GG.
europepmc +2 more sources
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.
Z K Eshkuvatov +2 more
exaly +3 more sources
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
exaly +4 more sources
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
exaly +3 more sources
Inexact Newton–Kantorovich Methods for Constrained Nonlinear Model Predictive Control
IEEE Transactions on Automatic Control, 2019 In this paper, we consider Newton–Kantorovich type methods for solving control-constrained optimal control problems that appear in model predictive control. Conditions for convergence are established for an inexact version of the Newton–Kantorovich method applied to variational inequalities. Based on these results, two groups of algorithms are proposed
Asen L Dontchev +2 more
exaly +2 more sources
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
doaj +1 more source
Was Harold Zurcher myopic after all? Replicating Rust's engine replacement estimates
Journal of Applied Econometrics, Volume 38, Issue 7, Page 1093-1100, November/December 2023., 2023 Summary Rust (1987) studies the dynamic decision making under uncertainty made by Harold Zurcher to replace bus engines. In the decades since, the model has been applied, extended, and used as an example multiple times. This paper resolves some discrepancies in how data were transformed in the original and subsequent archives.
Christopher Ferrall
wiley +1 more source