Paper's Title:

Euler Series Solutions for Linear Integral Equations

Author(s):

Mostefa Nadir and Mustapha Dilmi

Department of Mathematics,
University of Msila 28000,
ALGERIA.
E-mail: mostefanadir@yahoo.fr
E-mail: dilmiistapha@yahoo.fr

Abstract:

In this work, we seek the approximate solution of linear integral equations by truncation Euler series approximation. After substituting the Euler expansions for the given functions of the equation and the unknown one, the equation reduces to a linear system, the solution of this latter gives the Euler coefficients and thereafter the solution of the equation. The convergence and the error analysis of this method are discussed. Finally, we compare our numerical results by others.

Paper's Title:

Application of Chebyshev Polynomials to Volterra-Fredholm Integral Equations

Author(s):

Aissa Lakhal, Mostefa Nadir and Mohamed Nasseh Nadir

Department of Mathematics,
Faculty of Mathematics and
Informatics,
University of Msila,
Algeria.

E-mail: aissa.lakhal@univ-msila.dz
mostefa.nadir@univ-msila.dz
nadir.mohamednasseh@yahoo.com

URL: https://www.mostefanadir.com

Abstract:

The goal of this work is to examine the numerical solution of linear Volterra-Fredholm integral equations of the second kind using the first, second, third and fourth Chebyshev polynomials. Noting that, the approximate solution is given in the form of series which converges to the exact one. Numerical examples are compared with other methods, in order to prove the applicability and the efficiency of this technical.

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