Bulletin of Computational Applied Mathematics

20

Authors: Farkhondeh Hosseini Shekarabi, Reza Ezzati

This paper is concerned with the numerical solution of mixed Volterra-Fredholm integral equations, based on iterative method and two variable Bernstein polynomials. In the main result, this method has several benefits in proposing an efficient and simple scheme with good degree of accuracy. Our second main result is to prove the convergence of the method, and to derive an upper bound under assumptions. Numerical experiments are performed for the approximation of the solution of two examples to demonstrate the accuracy and integrity of the method.

22

Authors: Yamilet Quintana, Alejandro Urieles

This article deals with some properties -which are, to the best of our knowledge, new- of the generalized Euler polynomials of level $m$. These properties include a new recurrence relation satisfied by these polynomials and quadrature formulae of Euler-Maclaurin type based on them. Numerical examples are also given.

20

Authors: Seyyed Ahmad Edalatpanah

Milaszewicz, [Milaszewic J.P, Linear Algebra. Appl. 93,1987, 161$-$170] presented new preconditioner for linear system in order to improve the convergence rates of Jacobi and Gauss-Seidel iterative methods. Li et al.,[Li Y., Li C., Wu S., Appl. Math. Comput. 186, 2007, 379-388] applied this preconditioner and provided convergence theorem for modified AOR method. Yun and Kim [Yun J.H., Kim S.W., Appl. Math. Comput. 201, 2008, 56-64] pointed out some errors in Li et al.'s theorem and provided some correct results for convergence of the preconditioned AOR method. In this paper, we analyze their convergence properly and propose a new theorem for irreducible modified AOR method. In particular, based on directed graph, we prove that the convergence theorem of Li et al. is true, without any additional assumptions.

32

Authors: Muhammad Aslam Javed, Samina Ashraf, Syed Muhammad Husnine

In fuzzy logic, where members of a set might be linguistic terms, the degree of reflexivity might be in unit interval [0,1] instead of {0,1}. This behaviour of a fuzzy set plays an important role especially in the field of inclusion and similarity measure. This paper is aimed at discovering the relations between the parameters of Lukasiewicz transitive members of a family of cardinality-based fuzzy measure.

17

Authors: Saúl Buitrago, Olivo Rome

The aim of this work is to present the construction and use of Surrogate Reservoir Models capable of accurately predicting cumulative oil production for every well stimulated with cyclic steam injection at any given time in a heavy oil reservoir in Mexico considering uncertain variables. The central composite experimental design technique was selected to capture the maximum amount of information from the model response with a minimum number of reservoir models simulations. Four input uncertain variables (the dead oil viscosity with temperature, the reservoir pressure, the reservoir permeability and oil sand thickness hydraulically connected to the well) were selected as the ones with more impact on the initial hot oil production rate according to an analytical production prediction model. Twenty five runs were designed and performed with the STARS simulator for each well type on the reservoir model. The results show that the use of Surrogate Reservoir Models is a fast viable alternative to perform probabilistic production forecasting of the reservoir.

19

Authors: Esmail Hesameddini, Mehdi Shahbazi

In this paper, a reliable algorithm for solving the nonlinear Hammerstein integral equation arising from chemical phenomenon is presented. The conductor-like screening model for real solvents (COSMO-RS) integral equation will be solved by the shifted Legendre collocation method. This method approximates the unknown function with Legendre polynomials. The merits of this algorithm lie in the fact that, on the one hand, the problem will be reduced to a nonlinear system of algebraic equations. On the other hand, we show that the efficiency and accuracy of the shifted Legendre collocation method for solving these equations are remarkable. Also, this method is using a simple computational manner and its error analysis will be discussed by illustrating some theorems. Finally, two numerical experiments are given to confirm the superiority and efficiency of presented method with respect to some other well-known methods such as the Bernstein collocation method, Haar wavelet method and Sinc collocation method.

23

Authors: Bruno H. Cervelin, Dante Conti, Denise T. Detsch, Maria A. Diniz-Ehrhardt, José Mario Martínez

Intensive broiler production requires of accurate control systems aimed to maintain ideal conditions inside the facilities. The achievement of an appropriate environment guarantees good performance and sustainability of the production. Control and monitoring of temperature is a key factor during the production cycle. In countries with tropical and subtropical climate, such as Brazil, high values of temperatures can affect negatively the broiler production. Based on a temperature control model developed by the authors, this research is focused on the determination and fitting of the intrinsic parameters of the model. Consecutive executions of the model and changes in the facilities suggest adapting parameters constantly under the perspective of real-time systems. Four strategies of derivative-free optimization were applied to adjust the parameters of the model. Experiments were conducted with data collected from a pilot farm in South-eastern Brazil. Results demonstrated that the process of updating parameters needs to be implemented on the temperature control model. BOBYQA method resulted to be the best strategy to be taken into consideration for the improvement of the system.

24

Authors: Debora Cores, Johanna Figueroa

The well-known Conjugate Gradient (CG) method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG) method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.