Paper's Title:

Mapped Chebyshev Spectral Methods for Solving Second Kind Integral Equations on the Real Line

Author(s):

Ahmed Guechi and Azedine Rahmoune

Department of Mathematics, University of Bordj Bou Arréridj,
El Anasser, 34030, BBA,
Algeria.
E-mail: a.guechi2017@gmail.com
E-mail: a.rahmoune@univ-bba.dz

Abstract:

In this paper we investigate the utility of mappings to solve numerically an important class of integral equations on the real line. The main idea is to map the infinite interval to a finite one and use Chebyshev spectral-collocation method to solve the mapped integral equation in the finite interval. Numerical examples are presented to illustrate the accuracy of the method.

Paper's Title:

Numerical Study of a Mathematical Model of a Free-Surface Potential Flow

Author(s):

H. Serguine, F. Guechi and A. Gasmi

Department Of Mathematics, Faculty of Science,
Ferhat Abbas Universty, 19000, Setif,
Algeria.
E-mail: houria.serguine@univ-msila.dz

 
Department Of Mathematics, Faculty of Science,
Ferhat Abbas Universty, 19000, Setif,
Algeria.
E-mail:  fairouz.chegaar@univ-setif.dz

Laboratory of Pure and Applied Mathematics, Faculty of Mathematics and Computer Science,
Mohamed Boudiaf Universty, 28000, M'sila,
Algeria.
E-mail: abdelkader.gasmi@univ-msila.dz

Abstract:

In this work, the problem of a potential and two-dimensional flow with a free surface of an incompressible, irrotational and inviscid fluid of a jet in front an inclined wall is considered, where γ is the inclination angle with the horizontal. The shape of the free surface is presented by curves which are found numerically by the series truncation method. This technique is based on the conformal transformations, resulting with the surface tension effect T with the boundary conditions on the free surfaces given by Bernoulli's equation. The found results are dependant on parameters which are: the Weber's number α and the angle γ. For each Weber's number value, only one solution is specified and some shapes of free surfaces of the jet are illustrated.

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