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Documents published in Scipedia

• A Generalized Finite Difference-Volume Hybrid Method Applied to Shallow-Water Equations

  G. Tinoco Guerrero, F. Domínguez Mota, J. Tinoco-Ruiz, J. Martínez, N. Tinoco-Guerrero, M. Leppäranta, I. Mammarella

  Revista Mexicana de Métodos Numéricos (2020). Vol. 4, 2

  
  

  Abstract

  Due to the importance of the shallow-water equations in models of real-life phenomena, in recent years the study and model of problems that involve them have been the object of interest of many people. By reason of this, it is imperative to have efficient numerical methods to obtain an approximation of the solutions of the shallow-water equations. Several authors have worked in approximations using the well-known finite volume and finite element methods, nevertheless, even when these methods compute good approximations to real-life behavior, the computational cost is usually high, which could be a limitation to the application of these methods. This paper presents an explicit Generalized Finite Difference-Volume Hybrid approximation to the solution of the shallow-water equations, solved on irregular regions meshed with logically rectangular grids; the numerical results show the accuracy obtained with a low-cost implementation. The proposed scheme is a hybridization of a generalized finite difference scheme with the finite volume method.

  Abstract
  Due to the importance of the shallow-water equations in models of real-life phenomena, in recent years the study and model of problems that involve them have been the object [...]

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• Approximation to advection equation in plane irregular regions using a Method of Lines and Generalized Finite Differences

  G. Tinoco Guerrero, F. Domínguez Mota, J. Martínez, J. Tinoco-Ruiz

  Revista Mexicana de Métodos Numéricos (2018). Vol. 2, 3

  
  

  Abstract

  One of the greatest challenges in our days continues being to design numerical methods capable of approaching the solution of partial differential equations in a fast and precise way. One of the most important equations, due to the hydraulic and transport applications that it has, and the great amount of difficulties that it usually presents when resolving it numerically is the Advection Equation. In the present work we present a Method of Lines applied to the numerical solution of said equation in irregular regions making use of a Generalized Finite Differences scheme. A series of numerical tests and results are presented, which show the accuracy of the proposed method.

  Abstract
  One of the greatest challenges in our days continues being to design numerical methods capable of approaching the solution of partial differential equations in a fast and [...]

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Articles (Documents not available in Scipedia)

• A meshless finite difference scheme applied to the numerical solution of wave equation in highly irregular space regions

  Gerardo Tinoco-Guerrero, Heriberto Arias-Rojas, José Alberto Guzmán-Torres, Ricardo Román-Gutiérrez, José Gerardo Tinoco-Ruiz

  Tinoco-Guerrero, G., Arias-Rojas, H., Guzmán-Torres, J. A., Román-Gutiérrez, R., & Tinoco-Ruiz, J. G. (2023). A meshless finite difference scheme applied to the numerical solution of wave equation in highly irregular space regions. Computers & Mathematics with Applications, 136, 25-33. https://doi.org/10.1016/j.camwa.2023.01.035