Araceli Queiruga-Dios

Numerical algorithms for diffusion–reaction problems with non-classical conditions

Abstract Parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years. In this paper new high-order algorithms for the linear diffusion–reaction problem are derived. The convergence of the new schemes is studied and numerical examples are given to show the efficiency of the new methods to solve linear and nonlinear diffusion–reaction equations with these non classical conditions.

CAS and real life problems to learn basic concepts in Linear Algebra course

In this paper we examine the effect of the use of a Computer Algebra System (CAS) to solve interdisciplinary problems. We have been working for some years in the application of mathematics to different engineering problems, the main reason was to improve the motivation of our students and to make possible for them to connect and apply what they learn in Linear Algebra class to other engineering subjects. We describe a case study with students of Electromechanical and Mechanical Engineering from the Coimbra Institute of Engineering and from Geological and Industrial Engineering students from the University of Salamanca in a Linear Algebra course. The study involves the application of digital image processing to develop the basic skills of Linear Algebra. Furthermore, we include the results of a pre‐test and post‐test control group study using that application in the classroom. The results indicate that the experiences were very enriching for the students in different subjects. We tested at different centers from two different countries with similar results.

Variable step length algorithms with high-order extrapolated non-standard finite difference schemes for a SEIR model

Abstract In the present manuscript, higher-order methods are derived to solve a SEIR model for malware propagation. They are obtained using extrapolation techniques combined with nonstandard finite difference (NSFD) schemes used in Jansen and Twizell (2002). Thus, the new algorithms are more efficient computationally, and are dynamically consistent with the continuous model. Later, different procedures are considered to control the error in the discrete schemes. Numerical experiments are provided to illustrate the theory, and for the comparison of the different strategies in the adaptation of the variable step length.

Industrial Cyber-Physical Systems in Textile Engineering

Cyber-Physical Systems (CPS) is an emergent approach of physical processes, computer and networking, that focuses on the interaction between cyber and physical elements. These systems monitor and control the physical infrastructures, that is why they have a high impact in industrial automation. The implementation and operation of CPS just like the management of the resulting automation infrastructure is of key importance to the industry. The evolution towards Industry 4.0 is mainly based on digital technologies. We present the integration of Industry 4.0 within the textile industry.

Minecraft as a Tool in the Teaching-Learning Process of the Fundamental Elements of Circulation in Architecture

In this paper, we make a pedagogical proposal to study the basic elements of circulation in architecture undergraduate degrees, using the Minecraft game as a tool. The theoretical basis for the proposal are Vygotsky’s sociointeractional theory and Ausubel’s theory of meaningful learning. We find ourselves reflecting on Information and Communication Technologies (ICT), gamification and video games in education. We outline some basic elements about circulation in buildings, its types, functionality, and accessibility, and the creativity needed to solve circulation problems in architecture. We introduce the Minecraft game, its characteristics, elements and use it as educational tool. We conclude that video games, specifically Minecraft, are of high interest in education as they develop skills for problem solving, collaborative work, research motivation and proactivity.

A study on the efficiency and stability of high-order numerical methods for Form-II and Form-III of the nonlinear Klein–Gordon equations

In this paper, we discuss the problem of solving nonlinear Klein–Gordon equations (KGEs), which are especially useful to model nonlinear phenomena. In order to obtain more exact solutions, we have derived different fourth- and sixth-order, stable explicit and implicit finite difference schemes for some of the best known nonlinear KGEs. These new higher-order methods allow a reduction in the number of nodes, which is necessary to solve multi-dimensional KGEs. Moreover, we describe how higher-order stable algorithms can be constructed in a similar way following the proposed procedures. For the considered equations, the stability and consistency of the proposed schemes are studied under certain smoothness conditions of the solutions. In addition to that, we present experimental results obtained from numerical methods that illustrate the efficiency of the new algorithms, their stability, and their convergence rate.

Efficient high-order finite difference methods for nonlinear Klein-Gordon equations. I: Variants of the phi-four model and the form-I of the nonlinear Klein-Gordon equation

In this paper, the problem of solving some nonlinear Klein-Gordon equations (KGEs) is considered. Here, we derive different fourth- and sixth-order explicit and implicit algorithms to solve the phi-four equation and the form-I of the nonlinear Klein-Gordon equation. Stability and consistency of the proposed schemes are studied under certain conditions. Numerical results are presented and then compared with others obtained from some methods already existing in the scientific literature to explain the efficiency of the new algorithms. It is also shown that similar schemes can be proposed to solve many classes of nonlinear KGEs.

Case Study: Online Learning for Design and Calculation of Machines

In recent years, the University of Salamanca together with other 45 European universities have changed our university qualifications, resulting in substantial changes in the system of education. In this case study we detail the particular case of the subject of Design and Calculation of Machines of the Degree in Mechanical Engineering, which is given at the School of Industrial Engineering at the University of Salamanca. The use of technological tools and resources to make students acquire the desired competences suppose a change in the learning paradigm. The more traditional teaching system changes to become a self-learning system. With the files, tasks, and activities available on the web platform, students could follow their own learning. We include data related to the improvements in the students’ marks.

Project-based teaching in Calculus courses: Estimation of the surface and perimeter of the Iberian Peninsula

We have been working, for some years, in the application of mathematics to different engineering problems with the main goal of improving our students’ motivation and make possible for them to connect and apply what they learn in Calculus classes to other engineering subjects. We describe a case study with students of Electrotechnical Engineering from the Coimbra Institute of Engineering (ISEC) and from Biologist and Geological Engineering degrees students from the University of Salamanca (USAL) in a Calculus course. The study involves the application of mathematical software in the calculus of a real situation: the estimation of the surface and length of an irregular figure: the Iberian Peninsula. Furthermore, we include the results of a pre‐ and post‐test control group study, before and after using that application in the classroom. The results indicate that those experiences were very enriching for the students in different degrees and in both countries. We tested at different centers from two different countries with similar results.

A SEIR Model for Computer Virus Spreading Based on Cellular Automata.

There are a great variety of specimens of malware: computer viruses, computer worms, trojans, etc. Nowadays, malware is one of the most important computer security problem and the source of great financial losses. Consequently, it is necessary to design tools that allow one to simulate the behavior of malware propagation. These tools are based on mathematical models and the great majority of them tackle the study of a particular type of malware called computer worms. Nevertheless, to the best of our knowledge, there are few models devoted to the study of the spreading of computer viruses. In this sense, the main goal of this work is to introduce a new mathematical model, based on cellular automata, to analyze the epidemic behavior of computer virus. Specifically, it is a SEIR (Susceptible-Exposed-Infectious-Recovered) model where the nodes of the network are divided into four compartments: susceptible, exposed, infected and recovered.