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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2020 - 20248
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Autor: Negreanu, Mihaela × Tiene archivos: true ×

Resultados de la búsqueda

Mostrando 1 - 8 de 8
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    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/0000-0003-0533-3464
    We 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.
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    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 profile
    In 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.
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    Continuous and discrete periodic asymptotic behavior of solutions to a competitive chemotaxis PDEs system
    (Elsevier, 2021-04) Negreanu, Mihaela; Vargas Ureña, Antonio Manuel
    In 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.
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    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 Manuel
    In 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.
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    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 Manuel
    This 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.
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    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 Manuel
    We 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).
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    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 Manuel
    In 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.
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    Complex Ginzburg–Landau Equation with Generalized Finite Differences
    (MDPI, 2020-12-20) Salete Casino, Eduardo; Vargas Ureña, Antonio Manuel; García, Ángel; Negreanu, Mihaela; Benito Muñoz, Juan J.; Ureña, Francisco
    In this paper we obtain a novel implementation for irregular clouds of nodes of the meshless method called Generalized Finite Difference Method for solving the complex Ginzburg–Landau equation. We derive the explicit formulae for the spatial derivative and an explicit scheme by splitting the equation into a system of two parabolic PDEs. We prove the conditional convergence of the numerical scheme towards the continuous solution under certain assumptions. We obtain a second order approximation as it is clear from the numerical results. Finally, we provide several examples of its application over irregular domains in order to test the accuracy of the explicit scheme, as well as comparison with other numerical methods.