ORALS

SESSION: MathematicsSatAM-R6	4th Intl. Symp. on Sustainable Mathematics Applications
Sat Oct, 26 2019 / Room: Hermes (64/Mezz. F)
Session Chairs: Peter Rowlands; Avraam Konstantinidis; Session Monitor: TBA

12:35: [MathematicsSatAM04]
On The Convergence Of An Evolutionary Algorithm, Particle Swarm Optimization (PSO) And Its Application
Besiana Cobani¹ ; Aurora Ferrja¹ ; ¹University of Tirana, Tirana, Albania;
Paper Id: 451 [Abstract]

The evolutionary methods are optimization methods that converge to the global solution. There are many optimization techniques nowadays used and the one we are working is the evolutionary method PSO. Many authors have proposed various modifications of the basic PSO parameters with the goal to obtain a variant of PSO with best performance algorithm complexity. In our case, first, we present a modified PSO algorithm. Then we analyze the convergence of the proposed algorithm using differential equations. More precisely we relate a difference equation with a differential equation, and study the behavior of its solution. The solution brings results for the parameters of PSO, specifically for the coefficients of acceleration. Since the PSO results depend on its parameters, we propose new parametersthem based on the convergence study. We give an application in the energetic field in Albanian case, in the main three hydropower cascades of the country, which consist of three hydro power plants.

SESSION: MathematicsSatPM1-R6	4th Intl. Symp. on Sustainable Mathematics Applications
Sat Oct, 26 2019 / Room: Hermes (64/Mezz. F)
Session Chairs: Aurora Ferrja; Besiana Cobani; Session Monitor: TBA

14:00: [MathematicsSatPM105]
A Combination Of The Finite Element Method With GMRES To Obtain An Efficient Algorithm To Solve An Eigenvalue Problem
Aurora Ferrja¹ ; Besiana Cobani¹ ; ¹University of Tirana, Tirana, Albania;
Paper Id: 452 [Abstract]

To find an analytically solution of a problem involving a system of partial differential equation is a challenging tusk. So, we use iterative methods to obtain an approximate solution. In inverse scattering the transmission eigenvalue problem is important do determine data for the scatterer. From the complexity of the domain (scatterer) we use the finite element method because we can obtain the best approximation of the required zone. The problem we solve is nonlinear and non-selfadjoint. Using variational method and Fredholm alternative we transform it in order to be discretize. Colton and Cakoni give inferior and superior of the refractive index. This information is used in an inequality given by Colton and Haddar to determine a boundary for the eigenvalues involving the first Dirichlet eigenvalue as well. We use an algorithm to find the first eigenvalue. We have the refractive index n also The algorithm used is a combination of finite element method with GMRES algorithm.