UPM Institutional Repository

On solving an nxn system of nonlinear Volterra integral equations by the Newton-Kantorovich method


Citation

Hameed, Hameed Husam and Eshkuvatov, Zainidin K. and Nik Long, Nik Mohd Asri (2016) On solving an nxn system of nonlinear Volterra integral equations by the Newton-Kantorovich method. Science Asia, 42S (1). pp. 11-18. ISSN 1513-1874

Abstract

We consider an nxn system of nonlinear integral equations of Volterra type (nonlinear VIEs) arising from an economic model. By applying the Newton-Kantorovich method to the nonlinear VIEs we linearize them into linear Volterra type integral equations (linear VIEs). Uniqueness of the solution of the system is shown. An idea has been proposed to find the approximate solution by transforming the system of linear VIEs into a system of linear Fredholm integral equations by using sub-collocation points. Then the backward Newton interpolation formula is used to find the approximate solution at the collocation points. Each iteration is solved by the Nystrom type Gauss-Legendre quadrature formula (QF). It is found that by increasing the number of collocation points of QF with fewer iterations, a high accurate approximate solution can be obtained. Finally, an illustrative example is demonstrated to validate the accuracy of the method.


Download File

[img]
Preview
PDF
On solving an n × n system of nonlinear Volterra integral equations by the Newton-Kantorovich method.pdf

Download (6kB) | Preview

Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.2306 / scienceasia1513-1874.2016.42S.011
Publisher: Science Society of Thailand
Keywords: Nonlinear integral operator; Volterra integral type; Gauss-Legendre method
Depositing User: Nurul Ainie Mokhtar
Date Deposited: 30 Oct 2017 06:05
Last Modified: 30 Oct 2017 06:05
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.2306 / scienceasia1513-1874.2016.42S.011
URI: http://psasir.upm.edu.my/id/eprint/53428
Statistic Details: View Download Statistic

Actions (login required)

View Item View Item