Rui M P Almeida | Universidade da Beira Interior (original) (raw)

Papers by Rui M P Almeida

International Journal of Intelligence Science, 2012

Data Mining (DM) methods are being increasingly used in prediction with time series data, in addi... more Data Mining (DM) methods are being increasingly used in prediction with time series data, in addition to traditional statistical approaches. This paper presents a literature review of the use of DM with time series data, focusing on shorttime stocks prediction. This is an area that has been attracting a great deal of attention from researchers in the field. The main contribution of this paper is to provide an outline of the use of DM with time series data, using mainly examples related with short-term stocks prediction. This is important to a better understanding of the field. Some of the main trends and open issues will also be introduced.

Journal of Computational and Applied Mathematics

In this paper we make a study of a partial integral differential equation with p-Laplacian using ... more In this paper we make a study of a partial integral differential equation with p-Laplacian using a mixed finite element method. Two stable and convergent fixed point schemes are proposed to solve the nonlinear algebraic system. Using the implementation of the method in Matlab environment, we numerically analyse the convergence with an example. Some other examples are presented in order to illustrate several asymptotic behaviours and some localization effects of the solutions.

Journal of Computational and Applied Mathematics, 2021

Abstract In this paper, we consider a class of a nonlinear option pricing models considering tran... more Abstract In this paper, we consider a class of a nonlinear option pricing models considering transaction costs. The focus is on the numerical investigation of the Delta equation, where the unknown is the first spatial derivative of the option value. A numerical algorithm for solving a generalized Black–Scholes partial differential equation, which arises in European option pricing considering transaction costs is studied. The Crank–Nicolson method used to discretize in the temporal direction and the FEM used to discretize in the spatial direction are discussed in terms of accuracy, convergence and efficiency. The efficiency and accuracy of the proposed method are tested numerically, and the results confirm the theoretical behaviour of the solutions, which are also found to be in good agreement with the exact solution of the linear case.

Journal of the Operational Research Society, 2020

Abstract This paper addresses a shoe packing problem that is motivated by an industry application... more Abstract This paper addresses a shoe packing problem that is motivated by an industry application and involves two main stages: (i) packing shoes into suitable boxes and (ii) loading the packed shoes into three dimensional open-dimension containers. This is the first study dealing with the packing of small boxes into several containers where each container has all three dimensions open. Assigning shoes to a minimum number of box types is achieved using a 0–1 program, whereas the loading problem is tackled via a mixed-integer nonlinear program that minimizes the total volume of the container. That latter model is linearized by using a simple summation of the container dimensions, which is compared against a more elaborated linearization scheme. The effectiveness and efficiency of the proposed scheme are demonstrated with numerical experiments using real-world instances.

Resumo. No presente trabalho apresentamos uma aplicação computacional desenhada em Matlab para a ... more Resumo. No presente trabalho apresentamos uma aplicação computacional desenhada em Matlab para a resolução de sistemas de equações diferenciais com derivadas parciais, dependentes do tempo em domínios espaciais de dimensão 1. O algoritmo numérico baseia-se na formulação do método dos Elementos Finitos Móveis (MEFM) com funções de base não lineares e malhas adaptativas associadas a cada uma das variáveis dependentes. O principal objectivo desta nova implementação do MEFM é que possa ser utilizada de modo simples por um utilizador que não domine as técnicas da linguagem FORTRAN para resolver de modo eficiente uma grande variedade de problemas evolutivos, incluindo problemas com fronteiras móveis. Os exemplos numéricos que apresentamos permitem avaliar a robustez e performance deste código numérico escrito em Matlab e baseado no MEFM.

Empresa Y Sociedad Recurso Electronico Respondiendo Al Cambio Comunicaciones Presentadas 2007 Isbn 978 84 96648 10 4 Pag 91, 2007

Mathematics and Computers in Simulation, 2015

In this paper, we investigate the applicability of a moving mesh method when applied to the porou... more In this paper, we investigate the applicability of a moving mesh method when applied to the porous medium equation with variable exponent in 2D with free boundaries. The movement of the boundary is derived by a discretization of the Darcy law. The spatial discretization is defined by a partition in triangles of the domain, and the solution is approximated by piecewise polynomial functions of degree r ≥ 1 using Lagrange interpolating polynomials in area coordinates. A parabolic system of differential equations to control the movement of the interior vertices of the triangles is added to the equations of the problem. The resulting ordinary differential system of equations in time variable is solved using a suitable integrator. The integrals that arise in the system of ordinary differential equations are calculated using the Gaussian quadrature of appropriate order. Finally, we present a numerical application of this technique and compare the results with a fixed mesh method. c

The aim of this paper is to numerically study a class of nonlinear nonlocal degenerate parabolic ... more The aim of this paper is to numerically study a class of nonlinear nonlocal degenerate parabolic equations. The convergence and error bounds are proved for a linearized Crank-Nicolson-Galerkin finite element method with polynomial approximations of degree k > 1. Some explicit solutions are obtained and used to test the implementation of the method in Matlab environment.

In this work, we study the Dirichlet problem for a class of nonlinear coupled systems of reaction... more In this work, we study the Dirichlet problem for a class of nonlinear coupled systems of reaction-diffusion nonlocal type: We prove the existence and uniqueness of weak and strong solutions of these systems and localization properties of the solutions, including the waiting time effect. Moreover important results on polynomial and exponential decay and vanishing of the solutions in ﬁnite time are also presented. We improve the results obtained by Chipot and Lovart [5], Correa, Menezes and Ferreira [12], Raposo et al. [17] and ˆ Simsen and Ferreira [18] for coupled systems.

In this work, we study a system of parabolic equations with nonlocal nonlinearity of the followin... more In this work, we study a system of parabolic equations with nonlocal nonlinearity of the following type eq.. We prove the convergence of a linearized Euler-Galerkin nite element method and obtain the order of convergence. Finally, we implement and simulate the presented method in Matlab’s environment.

Computers & Chemical Engineering, 2005

The Chemical Engineering Science movement has served well in solving problems from micro to macro... more The Chemical Engineering Science movement has served well in solving problems from micro to macro scales. Ultimately, as Professor R. Sargent pointed out, it would be better if translated in "Scientific Engineering". Examples of innovation as a combination of science (concept), technology and process/product will be presented. The first example is perfusion chromatography based on the concept of "diffusivity augmented by convection" and on the technology of fabrication of large-pore packings. The second example, Simulated Moving Bed (SMB), is based on a concept developed to overcome the difficulties in implementing True Moving Bed processes. Technological contributions come from adsorbent materials and rotary valve to simulate the solid movement. SMB is now a key technology for chiral separations. Modelling/Simulation tools provide sound basis for design/operation by using the concept of "separation volume". The third example is from the area of multifunctional reactors. The SMB technology is extended to the simultaneous reaction/separation.

Applied Mathematics and Computation, 2014

ABSTRACT In this paper, we study the application of the moving mesh method to the porous medium e... more ABSTRACT In this paper, we study the application of the moving mesh method to the porous medium equation with absorption and variable exponents of nonlinearity in 2D domains with moving boundaries. The boundary's movement is governed by an equation prompted by the Darcy law and the spatial discretization is defined by a triangulation of the domain. At each finite element, the solution is approximated by piecewise polynomial functions of degree r >= 1 using Lagrange interpolating polynomials in area coordinates. The vertices of the triangles move according to a system of differential equations which is added to the equations of the problem. The resulting system is converted into a system of ordinary differential equations in time variable, which is solved using a suitable integrator. The integrals that arise in the system of ordinary differential equations are calculated using the Gaussian quadrature. Finally, we present some numerical results of application of this technique.

arXiv: Analysis of PDEs, 2020

In this paper, a class of nonlinear option pricing models involving transaction costs is consider... more In this paper, a class of nonlinear option pricing models involving transaction costs is considered. The diffusion coefficient of the nonlinear parabolic equation for the price VVV is assumed to be a linear function of the option's underlying asset price and the Gamma Greek VxxV_{xx}Vxx. The main aim of this work is to study the governing PDE of the Delta Greek. The existence of viscosity solutions is proved using the vanishing viscosity method. Regularizing the equation by adding a small perturbation to the initial problem, a sequence of approximate solutions uvarepsilonu^{\varepsilon}uvarepsilon is constructed and then the method of weak limits is applied to prove the convergence of the sequence to the viscosity solution of the Delta equation. The approximate problems constructed are shown to have good regularity, which allows the use of efficient and robust numerical methods.

Applied Numerical Mathematics, 2018

The aim of this paper is to establish convergence, properties and error bounds for the fully disc... more The aim of this paper is to establish convergence, properties and error bounds for the fully discrete solutions of a class of nonlinear systems of reaction-diffusion nonlocal type with moving boundaries, using the finite element method with polynomial approximations of any degree. A coordinate transformation which fixes the boundaries is used. Some numerical tests to compare our Matlab code with a moving finite element method are investigated.

Computers & Mathematics with Applications, 2017

The aim of this paper is the numerical study of a class of nonlinear nonlocal degenerate paraboli... more The aim of this paper is the numerical study of a class of nonlinear nonlocal degenerate parabolic equations. The convergence and error bounds of the solutions are proved for a linearized Crank-Nicolson-Galerkin finite element method with polynomial approximations of degree k ≥ 1. Some explicit solutions are obtained and used to test the implementation of the method in Matlab environment.

Journal of Computational and Applied Mathematics, 2016

In this work, we study a system of parabolic equations with nonlocal nonlinearity of the followin... more In this work, we study a system of parabolic equations with nonlocal nonlinearity of the following type        u t − a 1 (l 1 (u), l 2 (v))∆u + λ 1 |u| p−2 u = f 1 (x, t) in Ω×]0, T ] v t − a 2 (l 1 (u), l 2 (v))∆v + λ 2 |v| p−2 v = f 2 (x, t) in Ω×]0, T ] u(x, t) = v(x, t) = 0 on ∂Ω×]0, T ] u(x, 0) = u 0 (x), v(x, 0) = v 0 (x) in Ω , where a 1 and a 2 are Lipschitz-continuous positive functions, l 1 and l 2 are

IMA Journal of Applied Mathematics, 2016

In this work, we study the Dirichlet problem for a class of nonlinear coupled systems of reaction... more In this work, we study the Dirichlet problem for a class of nonlinear coupled systems of reaction-diffusion nonlocal type:        u t − a 1 (l 1 (u), l 2 (v))∆u + λ 1 |u| p−2 u = f 1 (x, t) in Ω×]0, T ] v t − a 2 (l 1 (u), l 2 (v))∆v + λ 2 |v| p−2 v = f 2 (x, t) in Ω×]0, T ] u(x, t) = v(x, t) = 0 on ∂Ω×]0, T ] u(x, 0) = u 0 (x), v(x, 0) = v 0 (x) in Ω .

In this work, we prove the existence and uniqueness of a strong regular solution for a certain cl... more In this work, we prove the existence and uniqueness of a strong regular solution for a certain class of a nonlinear coupled system of reaction-diffusion equations on a bounded domain with moving boundary. The exponential decay of the energy of the solutions, under the same assumptions, is also proved. In addition, we obtain approximate numerical solutions for systems of this type. In order to compare the theoretical and the numerical behaviour of the solutions, we

Nonlinear Analysis: Real World Applications, 2016

Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal d... more Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In particular, the finite time extinction and polynomial decay properties are proved.

Numerical Methods for Partial Differential Equations, 2014

The aim of this paper is to establish the convergence and error bounds for the fully discrete sol... more The aim of this paper is to establish the convergence and error bounds for the fully discrete solutions for a class of nonlinear equations of reaction-diffusion nonlocal type with moving boundaries, using a linearized Crank-Nicolson-Galerkin finite element method with polynomial approximations of any degree.

International Journal of Intelligence Science, 2012

Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics, 2021

Journal of the Operational Research Society, 2020

Empresa Y Sociedad Recurso Electronico Respondiendo Al Cambio Comunicaciones Presentadas 2007 Isbn 978 84 96648 10 4 Pag 91, 2007

Mathematics and Computers in Simulation, 2015

Computers & Chemical Engineering, 2005

Applied Mathematics and Computation, 2014

arXiv: Analysis of PDEs, 2020

Applied Numerical Mathematics, 2018

Computers & Mathematics with Applications, 2017

Journal of Computational and Applied Mathematics, 2016

In this work, we study a system of parabolic equations with nonlocal nonlinearity of the followin... more In this work, we study a system of parabolic equations with nonlocal nonlinearity of the following type        u t − a 1 (l 1 (u), l 2 (v))∆u + λ 1 |u| p−2 u = f 1 (x, t) in Ω×]0, T ] v t − a 2 (l 1 (u), l 2 (v))∆v + λ 2 |v| p−2 v = f 2 (x, t) in Ω×]0, T ] u(x, t) = v(x, t) = 0 on ∂Ω×]0, T ] u(x, 0) = u 0 (x), v(x, 0) = v 0 (x) in Ω , where a 1 and a 2 are Lipschitz-continuous positive functions, l 1 and l 2 are

IMA Journal of Applied Mathematics, 2016

In this work, we study the Dirichlet problem for a class of nonlinear coupled systems of reaction... more In this work, we study the Dirichlet problem for a class of nonlinear coupled systems of reaction-diffusion nonlocal type:        u t − a 1 (l 1 (u), l 2 (v))∆u + λ 1 |u| p−2 u = f 1 (x, t) in Ω×]0, T ] v t − a 2 (l 1 (u), l 2 (v))∆v + λ 2 |v| p−2 v = f 2 (x, t) in Ω×]0, T ] u(x, t) = v(x, t) = 0 on ∂Ω×]0, T ] u(x, 0) = u 0 (x), v(x, 0) = v 0 (x) in Ω .

Nonlinear Analysis: Real World Applications, 2016

Numerical Methods for Partial Differential Equations, 2014