Trends in Computational and Applied Mathematics
https://tema.sbmac.org.br/tema
<div><p dir="ltr"><span style="text-decoration: underline;"><strong><span class="issnLabel">ISSN online version:</span></strong> 2676-0029</span></p><p dir="ltr"><span><br /></span></p><p dir="ltr"><span>The journal </span><span>Trends in Applied and Computational Mathematics</span><span> - publishes original papers that present innovative applications and/or relevant contributions to the field of Applied and Computational Mathematics. The journal began in 1999 as an initiative of the Brazilian Society of Computational and Applied Mathematics - SBMAC - with the aim of publishing the Proceedings of the Brazilian National Conference on Computational and Applied Mathematics - CNMAC. At that time, the creation of the journal was an opportunity for the scientific community to expand the dissemination of the research presented at CNMAC. Later in 2006, with the growing demand for article publication by the Brazilian scientific community, the journal started receiving articles ahead-of-print, increasing the scope of this important publication.</span></p><p dir="ltr"><span>Since the beginning, the criteria to compose the journal’s Editorial Board were closely related to the concepts of competence, excellence and field of expertise, choosing renowned researchers from different regions from Brazil and also from abroad.</span></p><p dir="ltr"><span>The </span><span>Trends in Applied and Computational Mathematics </span><span>is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access.</span></p><p dir="ltr"><span>Submitted manuscripts should be original and follow the standards of international publishing. Manuscripts can be written in English or Portuguese. All articles should not exceed 20 pages in length, although longer papers may also be published under exceptional circumstances, at the discretion of the Editorial Board. The review is coordinated by the Editorial Board and carried out by at least two ad hoc reviewers, anonymously.</span></p><p dir="ltr"><span>Currently, one volume of the journal Trends in Computational and Applied Mathematics is published per year, which comprises up to four (4) fascicles (numbers). Since 2014, only institutional members receive printed copies of the journal. Institutional members are responsible for supplying copies to their respective libraries. The on-line version of the journal is available in PDF format with free access to other interested parties.</span></p><p dir="ltr"><span>In recent years, the Journal Trends in Computational and Applied Mathematics has received a large number of submissions in English language, both from Brazilian and foreign authors. This fact indicates its great recognition as an important publication in the field of Applied Mathematics, showing a great harmony with the national and international academic community. As a consequence, since 2012, the journal has been indexed in the SciELO database (</span><a href="http://www.scielo.br/tcam"><span>http://www.scielo.br/tcam</span></a><span>).</span></p><p dir="ltr"><span><img src="/public/site/images/lepidus/Capa.png" alt="" /></span></p><p dir="ltr"><span>All articles published in <strong>Trends in Computational and Applied Mathematics</strong> are licensed under a CC-BY license. </span></p><p dir="ltr"><span>Also, there is no APC (Article Publishing Charge) fee.</span></p></div><p><a href="/tema/about/submissions#onlineSubmissions" target="_self"><strong>SUBMIT AN ARTICLE TO TCAM</strong></a></p>SBMACen-USTrends in Computational and Applied Mathematics2676-0029<p dir="ltr"><span>Authors who publish in this journal agree to the following terms: </span></p><ol><li dir="ltr"><p dir="ltr"><span>Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the </span><a href="http://creativecommons.org/licenses/by/3.0/"><span>Creative Commons Attribution License</span></a><span> that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal. </span><span><br /></span></p></li><li dir="ltr"><p dir="ltr"><span>Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal. </span><span><br /></span><span> </span></p></li><li dir="ltr"><p dir="ltr"><span>Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See </span><a href="http://opcit.eprints.org/oacitation-biblio.html"><span>The effect of open access</span></a><span>).</span></p></li><li dir="ltr"><p dir="ltr"><span><span>This is an open access journal which means that all content is freely </span><span>available without charge to the user or his/her institution. Users are </span><span>allowed to read, download, copy, distribute, print, search, or link to </span><span>the full texts of the articles, or use them for any other lawful </span><span>purpose, without asking prior permission from the publisher or the</span><br /><span>author. This is in accordance with the BOAI definition of open access</span></span></p></li></ol><p> </p><p><strong>Intellectual Property</strong></p><p>All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.</p>Métodos de Análise de Decisão Multicritério para Seleção de Padrões de Corte
https://tema.sbmac.org.br/tema/article/view/1527
<p>Em indústrias de manufatura, um dos processos de produção consiste em cortar grandes objetos em peças menores. Em pesquisa operacional, o estudo desse processo é conhecido como o problema de corte de estoque (PCE) e, devido à sua dificuldade de resolução, métodos heurísticos vêm sendo desenvolvidos pelos pesquisadores da área. Neste trabalho, propomos utilizar técnicas de análise de decisão multicritério (MCDA) a fim de resolver o PCE de forma eficiente em termos de GAP e tempo computacional. Nossa estratégia consiste em selecionar previamente os melhores padrões de corte com técnicas MCDA e resolver o problema apenas com esses padrões selecionados. Os testes computacionais mostraram que a solução obtida com essa estratégia apresenta um GAP entre 0,25% e 4,25% quando comparada com a solução ótima, dando indícios da qualidade da abordagem proposta. </p>B. S. C. CampelloC. T. L. S. Ghidini
Copyright (c) 2022 TEMA (São Carlos)
2022-03-252022-03-2523111610.5540/tcam.2022.023.01.00001Fuzzy Boundary for Beams Vibrations in Vehicles
https://tema.sbmac.org.br/tema/article/view/1514
The aim of this work is to study the transversal motion of a car's chassis, modeled by a beam and supported at its ends by two set of spring-damper element. We use a finite differences method with Robin boundary conditions at the ends to solve the mathematical modeling. The boundary conditions constants are modeled by a fuzzy parameter, which is obtained through Fuzzy Rule-Based System (FRBS) acting on the different vibrations of the model depending on the number of spirals and time of use of the spring. The contributions in this study come in the sense of considering the elastic constant of the spring as a relevant instrument acting in the system, because the analytical formula to perform these calculations does not take into consideration the time of use of it. Indeed, the mechanical components of the vehicle might have their properties altered due to fatigue process, for example. The impacts of the property evolution in the car dynamics might induce undesirable passenger's discomfort up to the vehicle performance lost. The results showed that the time of use of the spring influences the displacement of the vehicle, due to the loss of stiffness, thus affecting its stability.M. P. S. FerreiraR. M. JafeliceL. Sanches
Copyright (c) 2022 TCAM
2022-03-252022-03-25231173110.5540/tcam.2022.023.01.000017Construction of Complex Lattice Codes via Cyclotomic Fields
https://tema.sbmac.org.br/tema/article/view/1584
Through algebraic number theory and Construction $A$ we extend an algebraic procedure which generates complex lattice codes from the polynomial ring \mathbb{F}_{2}[x]/(x^{n}-1), where \mathbb{F}_{2}=\{0,1\}, by using ideals from the generalized polynomial ring \frac{\mathbb{F}_{2}[x,\frac{1}{2}\mathbb{Z}_{0}]}{((x^{\frac{1}{2}})^{n}-1)} through the ring of integers $\mathcal{O}_{\mathbb{L}}$ of the cyclotomic field \mathbb{L}=\mathbb{Q}(\zeta_{2^{s}}), where \zeta_{2^{s}} is a 2^{s}-th root of the unit, with s>2.E. D. CarvalhoA. A. AndradeT. ShahC. C. Trinca
Copyright (c) 2022 Trends in Computational and Applied Mathematics
2022-03-252022-03-25231335010.5540/tcam.2022.023.01.00033Hybrid Quaternions of Leonardo
https://tema.sbmac.org.br/tema/article/view/1582
<p>In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo,<br />quaternions and hybrid numbers were presented. Soon after, its recurrence, characteristic equation, its relation with the Fibonacci quaternions, generating function, Binet’s formula, as well as its extension to non-positive integer indices were developed. Finally, identities involving Leonardo’s hybrid quaternions are presented.</p>M. C. S. MangueiraF. R. V. AlvesP. M. M. C. Catarino
Copyright (c) 2022 Trends in Computational and Applied Mathematics
2022-03-252022-03-25231516210.5540/tcam.2022.023.01.00051Strong Stability Preserving Runge-Kutta Methods Applied to Water Hammer Problem
https://tema.sbmac.org.br/tema/article/view/1469
<p>The characteristic method of lines is the most used numerical method applied to the water hammer problem. It transforms a system of partial differential equations involving the independent variables time and space in two ordinary differential equations along the characteristics curves and then solve it numerically. This approach, although showing great stability and quick execution time, creates ∆x-∆t dependency to properly model the phenomenon. In this article we test a different approach, using the method of lines in the usual form, without the characteristics curves and then applying strong stability preserving Runge-Kutta Methods aiming to get stability with greater ∆t.</p>D. F. G. SantiagoA. F. AntunisD. R. TrindadeW. J. S. Brandão
Copyright (c) 2022 TCAM
2022-03-252022-03-25231637710.5540/tcam.2022.023.01.00063Numerical Analysis and Approximate Travelling Wave Solutions for a Higher Order Internal Wave System
https://tema.sbmac.org.br/tema/article/view/1518
<p>In this work we focus on the numerical solution of a higher order bidirectional nonlinear model of Boussinesq type involving a nonlocal operator. Based on a von Neumann stability analysis for the linearized problem, an efficient and stable scheme for the nonlinear system is proposed. Our method is based on a numerical scheme known from the literature that solves satisfactorily a lower order linear system. Additionally, approximate periodic travelling wave solutions profiles for the higher order nonlinear system are presented. Such approximate travelling wave solutions are obtained from a solitary wave family of solutions for the Intermediate Long Wave (ILW) equation and the regularized Intermediate Long Wave (rILW) equation.</p>W. C. LesinhovskiA. Ruiz de Zárate
Copyright (c) 2022 TCAM
2022-03-252022-03-252317910010.5540/tcam.2022.023.01.00079A Mathematical Model for Accessing Dengue Hemorrhagic Fever in Infants
https://tema.sbmac.org.br/tema/article/view/1417
<span>A mathematical model was developed to describe the dynamics of the primary infection of dengue virus in infant who were born of a mother immune to some serotype of the dengue virus. The model is given by a system of nonlinear ordinary differential equations with the time-dependent variables for the number of DENV antibodies of the infant transferred from their immune, uninfected and infected monocytes and dengue virus. The mathematical analysis was carried out where the conditions for the existence of the disease-free equilibrium and the endemic equilibrium were established. The numerical simulations were performed considering different scenarios for R0 (Basic Reproductive Number), illustrating the global convergence of the numerical results for the equilibrium points. The results are in agreement with our derived global stability analysis. It can be concluded that the DHF in the infants could occur in the peaks observed for the infected monocytes and dengue virus.</span>F. A. CamargoT. M. OliveiraD. S. RodriguesP. F. A. ManceraF. L. P. Santos
Copyright (c) 2022 TCAM
2022-03-252022-03-2523110111510.5540/tcam.2022.023.01.00101Código Computacional Avançado para Análise de Fenômenos Físicos de Campo Escalar da Engenharia
https://tema.sbmac.org.br/tema/article/view/1506
As equações diferenciais governam inúmeros fenômenos físicos presentes em diversos campos de conhecimento da física-matemática. Uma vez que os modelos são compreendidos pela teoria de campo escalar, possibilitam a descrição de uma gama de aplicações práticas da engenharia, transitando de problemas na área da acústica, térmica, mecânica dos sólidos e fluidos, eletromagnetismo, dentre outras. Neste cenário, o vigente artigo concentra-se em apresentar o módulo específico do programa computacional, desenvolvido em Matlab, denominado NASEN, destinado à solução da equação de campo escalar por meio do método dos elementos finitos (MEF). Para tanto, a discretização do espacial é realizada com base nos procedimentos matemáticos do método de Galerkin e a discretização temporal é realizado com base no método de integração de Newmark e o método-theta. Estuda-se problemas de diferentes naturezas, como problemas parabólicos não lineares, hiperbólicos e de autovalor. A metodologia empregada para solução dos problemas não lineares tem como base as estratégias incrementais e iterativas de Newton-Raphson. A avaliação de desempenho do programa computacional é realizada com as soluções analíticas, numéricas ou experimentais disponíveis na literatura. Em síntese, os resultados obtidos mostram-se satisfatórios, indicando que o código computacional é capaz de prever adequadamente os comportamentos físicos dos problemas propostos.N. S. Neves
Copyright (c) 2022 TEMA (São Carlos)
2022-03-252022-03-2523111714210.5540/tcam.2022.023.01.00117A SIR Model with Spatially Distributed Multiple Populations Interactions for Disease Dissemination
https://tema.sbmac.org.br/tema/article/view/1572
In this contribution we analyze a discretized SIR (Susceptible, Infectious, and Removed) compartmental model, to investigate the role of individual interactions in the spread of diseases. The compartments <em>S</em>_{<em>i</em>, <em>j</em>}, <em>I</em>_{<em>i</em>,<em>j</em>} and <em>R</em>_{<em>i</em>, <em>j</em>} (<em>i</em>, <em>j</em>, = 1,2, ..., <em>n</em>) are spatially distributed in a two-dimensional <em>n</em> x <em>n</em> network. We assume that the dynamics follow the well-known SIR-like iteration within the population in each (<em>i</em>,<em>j</em>) site. Moreover, the dynamics are enriched by considering a multi-population interaction following a Gaussian spatial distribution. Therefore, the mobility of individuals between distinct networks is measured from the width alpha of the Gaussian distribution. The interaction of individuals between distinct sites, responsible for the contagion between different populations, is assumed to occur in a time interval smaller than a fixed interval $h$ so that, the total population in each site (<em>i</em>, <em>j</em>), given by <em>N</em>_{<em>i</em>, <em>j</em>} =<em>S</em>_{<em>i</em>, <em>j</em>} + <em>I</em>_{<em>i</em>, <em>j</em>} + <em>R</em>_{<em>i</em>, <em>j</em>}, remained constant (for example, individual leaves his home site (<em>i</em>, <em>j</em>) to work at a neighboring site and returns to his home in a time interval less than <em>h</em> ). We numerically explore some scenarios of population interaction, based on distinct choices of width alpha, that include a hypothetically rapidly closedness and reopening of the economy. The results found show interesting dynamics in the infected population due to the interaction parameter alpha(<em>t</em>) between the populations. Finally, the model can be applied to evaluate the spread of diseases such as COVID-19 enabling decision making in different contexts.<br /><br /><br />J. C. MarquesA. De CezaroM. J. Lazo
Copyright (c) 2022 Trends in Computational and Applied Mathematics
2022-03-252022-03-2523114315410.5540/tcam.2022.023.01.00143Estimativa de Parâmetros e Solução de um Problema de Transferência de Calor Utilizando Métodos de Otimização Modificados
https://tema.sbmac.org.br/tema/article/view/1481
<p>Neste artigo é realizada a estimativa de parâmetros e solução de um problema de transferência de calor, onde os resultados numéricos são comparados com dados experimentais obtidos na literatura. O modelo matemático é resolvido numericamente utilizando o Método das Diferenças Finitas (MDF) com formulações explícita e implícita. Já a estimativa dos parâmetros é feita utilizando os métodos de otimização estocástica Luus-Jaakola (LJ) e Algoritmo de Colisão de Partículas (do inglês, Particle Collision Algorithm - PCA), bem como modificações propostas nos referidos métodos. Os resultados obtidos foram satisfatórios tendo as modificações apresentado uma redução do número de avaliações da função objetivo (NAF) necessários para encontrar os parâmetros de interesse, bem como possibilitou um bom ajuste entre as temperaturas obtidas experimentalmente e resultados numéricos, motivando novas aplicações em problemas de mesma natureza.</p>A. T. SilvaW. R. TellesG. S. Semaan
Copyright (c) 2022 TEMA (São Carlos)
2022-03-252022-03-2523115517410.5540/tcam.2022.023.01.00155What if the Forecaster Knew: Assessing Forecast Reliability Via Simulation
https://tema.sbmac.org.br/tema/article/view/1578
<p>The FIFA Men’s World Cup (FWC) is the most important football (soccer) competition, attracting worldwide attention. A popular practice among football fans in Brazil is to organize contests in which each participant informs guesses on the final score of each match. The participants are then ranked according to some scoring rule. Inspired by these contests, we created a website to hold an online contest, in which participants were asked for their probabilities on the outcomes of upcoming matches of the FWC. After each round of the tournament, the ranking of all participants based on a proper scoring rule was published. In this article we estimate, by means of simulations, the ability of the best forecasters of our contest, considering that their good performances could be due to randomness. We also study the performance of some methods to aggregate individual forecasts, in order to study if some sort of wisdom of crowds (WOC) phenomenon was verified in the contest.</p>M. InacioR. IzbickiD. LopesM. A. DinizL. E. SalasarJ. C. P. Ferreira
Copyright (c) 2022 Trends in Computational and Applied Mathematics
2022-03-252022-03-2523117519210.5540/tcam.2022.023.01.00175Modeling and Computer Simulation of Viscoelastic Crypt Deformation
https://tema.sbmac.org.br/tema/article/view/1566
<p>Colorectal cancer morphogenesis begins at the cellular level from cell mutations in the intestinal epithelium cavities called crypts. These mutations lead to a pressure difference in the epithelium crypt walls, which causes deformation and generates visible abnormalities in the epithelium. The geometrical modeling of these crypts and the mathematical modeling of the physical process that cause the deformations can be simulated by using a Finite Element Method. The method solves numerically the system of PDE equations that governs this phenomenon and permits to estimate the deformations of the crypt walls. We simulate in this work the crypt deformation when the cell mutations appear in several regions of the crypt epithelium.</p>E. P. OliveiraG. Romanazzi
Copyright (c) 2022 Trends in Computational and Applied Mathematics
2022-03-252022-03-2523119321110.5540/tcam.2022.023.01.00193