Persona: Vargas Ureña, Antonio Manuel
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Vargas Ureña
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Antonio Manuel
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Publicación Generalized finite difference method applied to solve seismic wave propagation problems. Examples of 3D simulations(Wiley, 2023) Flores, Jesús; Salete Casino, Eduardo; Benito Muñoz, Juan J.; Vargas Ureña, Antonio Manuel; Conde, Eduardo R.; https://orcid.org/0000-0001-5201-4277The simulation of seismic wave propagation generally requires dealing with complex tridimensional geometries that are irregular in shape 11 and have non-uniform properties, features that make interesting the application of the generalized finite difference method in this field. 12 This work continues the extensive developments by the research team focused on the simulation of seismic wave propagation in two-13 dimensional domains. In this new contribution, the general formulation and the treatment of free surface boundary conditions are 14 extended for the three-dimensional case and the results obtained from different examples are analyzed.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 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 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.Publicación An effective numeric method for different formulations of the elastic wave propagation problem in isotropic medium(Elsevier, 2021-08) Salete Casino, Eduardo; Vargas Ureña, Antonio Manuel; García, Ángel; Benito Muñoz, Juan J.; Ureña, Francisco; Ureña, MiguelThis paper shows how the Generalized Finite Difference Method allows the same schemes in differences to be used for different formulations of the wave propagation problem. These formulations present pros and cons, depending on the type of boundary and initial conditions at our disposal and also the variables we want to compute, while keeping additional calculations to a minimum. We obtain the explicit schemes of this meshless method for different possible formulations in finite differences of the problem. Criteria for stability and convergence of the schemes are given for each case. The study of the dispersion of the phase and group velocities presented in previuos paper of the authors is also completed here. We show the application of the propounded schemes to the wave propagation problem and the comparison of the efficiency, convenience and accuracy of the different formulations.Publicación 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, FranciscoIn 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.