Abstract and Applied Analysis

On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation

Abstract

We develop the Newton-Kantorovich method to solve the system of $2\times2$ 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. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.

Article information

Source
Abstr. Appl. Anal., Volume 2015, Special Issue (2015), Article ID 219616, 12 pages.

Dates
First available in Project Euclid: 16 June 2015

https://projecteuclid.org/euclid.aaa/1434459240

Digital Object Identifier
doi:10.1155/2015/219616

Mathematical Reviews number (MathSciNet)
MR3339663

Zentralblatt MATH identifier
1352.65652

Citation

Husam Hameed, Hameed; Eshkuvatov, Z. K.; Ahmedov, Anvarjon; Nik Long, N. M. A. On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation. Abstr. Appl. Anal. 2015, Special Issue (2015), Article ID 219616, 12 pages. doi:10.1155/2015/219616. https://projecteuclid.org/euclid.aaa/1434459240

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