A meshless method based on the moving least squares (MLS) approximation for the numerical solution of two-dimensional linear integral equations of the second kind on non-rectangular domains

Zahra El Majouti; Rachid El Jid; Abdelkarim Hajjaj; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 62

A meshless method based on the moving least squares (MLS) approximation for the numerical solution of two-dimensional linear integral equations of the second kind on non-rectangular domains

Zahra El Majouti, Rachid El Jid, Abdelkarim Hajjaj

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Jan 17, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: In this paper, we present a numerical method for solving two-dimensional linear Fredholm integral equations of the second kind on a non-rectangular domain.The scheme utilizes the shape functions of the moving least squares (MLS) approximation constructed on scattered points as a basis in the discrete collocation method. The MLS methodology is an effective technique for approximating unknown functions which involves a locally weighted least square polynomial fitting. The proposed method is meshless, since it does not need any background mesh or cell structures and so it is independent of the ...