2024 : 6 : 14
Somayeh Nemati

Somayeh Nemati

Academic rank: Associate Professor
ORCID:
Education: PhD.
ScopusId:
Faculty: Faculty of Mathematical Sciences
Address:
Phone: 01135302419

Research

Title
Legendre Expansion Methods for the Numerical Solution of Nonlinear 2D Fredholm Integral Equations of the Second
Type
JournalPaper
Keywords
Two-dimensional Fredholm integral equation, Legendre polynomials, best approximation, polynomial interpolation.
Year
2013
Journal Journal of Applied Mathematics and Informatics
DOI
Researchers Somayeh Nemati ، Yadollah Ordokhani

Abstract

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.