Persona: Vargas Ureña, Antonio Manuel
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0000-0002-2235-0111
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Vargas Ureña
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Antonio Manuel
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Publicación On the numerical solution to space fractional differential equations using meshless finite differences(Elsevier, 2024-10-28) García, A.; Negreanu, M.; Ureña, F.; Vargas Ureña, Antonio ManuelWe derive a discretization of the Caputo and Riemann–Liouville spatial derivatives by means of the meshless Generalized Finite Difference Method, which is based on moving least squares. The conditional convergence of the method is proved and several examples over one dimensional irregular meshes are given.Publicación Solving a chemotaxis-haptotaxis system in 2D using Generalized Finite Difference Method(ScienceDirect, 2020-05-27) Benito Muñoz, Juan J.; García Hernández, Miguel Ángel; Gavete Corvinos, Luis Antonio; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio Manuel; https://orcid.org/0000-0002-9092-9619; https://orcid.org/0000-0001-6581-5671; https://orcid.org/0000-0003-0533-3464We study a mathematical model of cancer cell invasion of tissue (extracellular matrix) consisting of a system of reaction-diffusion-taxis partial differential equations which describes the interactions between cancer cells, the matrix degrading enzyme and the host tissue. We analyze the local stability of the constant equilibrium solutions to the chemotaxis-haptotaxis system, we derive a discretization of the system by means of the Generalized Finite Difference Method (GFDM) and we prove the convergence of the discrete solution to the analytical one. Also, we provide several numerical examples on the applications of this meshless method over regular and irregular domains.Publicación Numerical solution of a hydrodynamic model with cavitation using finite difference method at arbitrary meshes(ScienceDirect, 2024-07-25) García Hernández, Miguel Ángel; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio Manuel; https://orcid.org/0000-0003-0533-3464 View this author’s ORCID profileIn this paper, we investigate the implementation of the finite difference method on arbitrary meshes in conjunction with a fixed-point algorithm for the lubrication problem of a journal bearing with cavitation, considering the Elrod-Adams model. We establish numerical properties of the generalized finite difference scheme and provide several illustrative examples.Publicación Continuous and discrete periodic asymptotic behavior of solutions to a competitive chemotaxis PDEs system(Elsevier, 2021-04) Negreanu, Mihaela; Vargas Ureña, Antonio ManuelIn this paper we study the continuous and full discrete versions of a parabolic-parabolic-elliptic system with periodic terms that serves as a model for some chemotaxis phenomena. This model appears naturally in the interaction of two biological species and a chemical. The presence of the periodic terms has a strong impact on the behavior of the solutions. Some conditions on the system’s data are given that guarantee the global existence of solutions that converge to periodical solutions of an associated ODE’s system. Further, we analyze the discretized version of the model using a Generalized Finite Difference Method (GFDM) and we confirm that the properties of the continuous model are also preserved for the resulting discrete model. To this end, we prove the conditional convergence of the numerical model and study some practical examples.Publicación On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences(Elsevier, 2020-04) Benito Muñoz, Juan J.; García, Ángel; Gavete, Luis; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio ManuelIn the present paper we propose the Generalized Finite Difference Method (GFDM) for numerical solution of a cross-diffusion system with chemotactic terms. We derive the discretization of the system using a GFD scheme in order to prove and illustrate that the uniform stability behavior/ convergence of the continuous model is also preserved for the discrete model. We prove the convergence of the explicit method and give the conditions of convergence. Extensive numerical experiments are presented to illustrate the accuracy, efficiency and robustness of the GFDM.Publicación On the numerical solution to a Solow model with spatial diffusion and technology-induced capital mobility(ScienceDirect, 2023-10-12) Ureña, N.; Vargas Ureña, Antonio ManuelThis work studies a parabolic-parabolic PDE system that describes the evolution of physical capital (denoted by ”k”) and technological progress (denoted by ”A”). The study employs a meshless method in one and two- dimensional bounded domains with regular boundaries. The well-known Solow model is extended to consider the spatial diffusion of both capital and technology. Additionally, we study the case in which induced movement of capital towards regions with a large technological progress occurs. For such models, we propose schemes based on the Generalized Finite Difference method and prove the convergence of the numerical solution to the continuous one, which is the main objective of the study. Several examples show the dynamics of the model for a wide range of parameters, illustrating the accuracy of the numerical method.Publicación Numerical solution to a Parabolic-ODE Solow model with spatial diffusion and technology-induced motility(ScienceDirect, 2024-04-08) Ureña, N.; Vargas Ureña, Antonio ManuelThis work studies a parabolic-ODE PDE’s system which describes the evolution of the physical capital “k” and technological progress “A”, using a meshless method in one and two dimensional bounded domain with regular boundary. The well-known Solow model is extended by considering the spatial diffusion of both capital and technology. Moreover, we study the case in which no spatial diffusion of the technology progress occurs. For such models, we propound schemes based on the Generalized Finite Difference method and prove the convergence of the numerical solution to the continuous one. Several examples show the dynamics of the model for a wide range of parameters. These examples illustrate the accuary of the numerical method.Publicación Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method(Elsevier, 2020-11) Benito Muñoz, Juan J.; García, Ángel; Gavete, Luis; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio ManuelThis work studies a parabolic-parabolic chemotactic PDE's system which describes the evolution of a biological population “U” and a chemical substance “V”, using a Generalized Finite Difference Method, in a two dimensional bounded domain with regular boundary. In a previous paper [12], the authors asserted global classical solvability and periodic asymptotic behavior for the continuous system in 2D. In this continuous work, a rigorous proof of the global classical solvability to the discretization of the model proposed in [12] is presented in two dimensional space. Numerical experiments concerning the convergence in space and in time, and long-time simulations are presented in order to illustrate the accuracy, efficiency and robustness of the developed numerical algorithms.Publicación Two finite difference methods for solving the Zakharov–Kuznetsov-Modified Equal-Width equation(Elsevier, 2023-08) Benito Muñoz, Juan J.; García, Ángel; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio ManuelWe derive the implementation of two meshless methods, the Space–Time Cloud Method and the Generalized Finite Difference Method, for solving the Zakharov–Kuznetsov-Modified Equal-Width equation, a nonlinear wave equation used to model the propagation of waves in nonuniform media. Also, we prove convergence of the GFD explicit scheme. We compare both methods in terms of accuracy and efficiency (execution times).Publicación Solving a reaction-di usion system with chemotaxis and non-local terms using Generalized Finite Di erence Method. Study of the convergence(Elsevier, 2021-06) Benito Muñoz, Juan J.; García, Ángel; Gavete, Luis; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio ManuelIn this paper a parabolic–parabolic chemotaxis system of PDEs that describes the evolution of a population with non-local terms is studied. We derive the discretization of the system using the meshless method called Generalized Finite Difference Method. We prove the conditional convergence of the solution obtained from the numerical method to the analytical solution in the two-dimensional case. Several examples of the application are given to illustrate the accuracy and efficiency of the numerical method. We also present two examples of a parabolic–elliptic model, as generalized by the parabolic–parabolic system addressed in this paper, to show the validity of the discretization of the non-local terms.