Documents published in Scipedia

• Boletín de la Sociedad Mexicana de Computación Científica y sus Aplicaciones (2021)

  G. Tinoco Guerrero, J. Guzmán Torres, J. Alavez, J. Tinoco-Ruiz

  Gerardo Tinoco-Guerrero's personal collection (2022). 1

  
  

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• An Implicit Modified Lax-Wendroff Scheme for Irregular 2D Space Regions

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

  IMACS Series in Computational and Applied Mathematics (2013).

  
  

  Abstract

  Nowadays, there are many modelling problems which involve the shallow water equations for irregular domains. One of the most important blocks for solving these equations is the advection equation. In this paper, we present the implementation of an implicit modified Lax-Wendroff scheme in order to approximate the solution of the advection equation in some irregular domains in the plane, using a general finite difference method on structured convex grids.

  Abstract
  Nowadays, there are many modelling problems which involve the shallow water equations for irregular domains. One of the most important blocks for solving these equations is [...]

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• Numerical solution of diffusion equation using a method of lines and generalized finite differences

  G. Tinoco Guerrero, F. Domínguez Mota, J. Guzmán Torres, J. Tinoco-Ruiz

  Rev. int. métodos numér. cálc. diseño ing. (2022). Vol. 38, (2), 24

  
  

  Abstract

  One of the greatest challenges in the area of applied mathematics continues to be the design of numerical methods capable of approximating the solution of partial differential equations quickly and accurately. One of the most important equations, due to the hydraulic and transport applications it has, and the large number of difficulties that it usually presents when solving it numerically is the Diffusion Equation.   In the present work, a Method of Lines applied to the numerical solution of the said equation in irregular regions is presented using a scheme of Generalized Finite Differences. The second-order finite difference method uses a central node and 8 neighbor points in order to address the spatial approximation. A series of tests and numerical results are presented, which show the accuracy of the proposed method.

  Abstract
  One of the greatest challenges in the area of applied mathematics continues to be the design of numerical methods capable of approximating the solution of partial differential [...]

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• Numerical Solution of Advection Equations Using Structured Grids on Plane Irregular Regions With a Finite Differences Scheme

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

  SMCCA (2015). 20

  
  

  Abstract

  Today we faced the problem of solving equations for shallow bodies of water in irregular regions; These equations are very important to be able to model the behavior of liquids that have the characteristic that their extension is much greater than their depth. One of the important blocks to solve these equations is the advection equation. In this work, some schemes are proposed to approximate the solution of the advection equation in irregular regions in the plane, using a variation of the finite difference method in convex and structured meshes.

  Abstract
  Today we faced the problem of solving equations for shallow bodies of water in irregular regions; These equations are very important to be able to model the behavior of liquids [...]

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• Generalized finite difference solution for the Motz Problem

  C. Chávez, F. Domínguez Mota, S. Lucas-Martinez, J. Tinoco-Ruiz, D. Santana Quinteros

  Rev. int. métodos numér. cálc. diseño ing. (2021). Vol. 37, (1), 13

  
  

  Abstract

  In this paper, it is presented a formulation of a generalized finite difference scheme to solve the Motz problem. It is based on a general difference scheme defined by an optimality condition, which has been developed to solve Poisson-like equations whose domains are approximated by a wide variety of grids over general regions. Numerical examples showing second-order accuracy of the calculated solutions are presented.

  Abstract
  In this paper, it is presented a formulation of a generalized finite difference scheme to solve the Motz problem. It is based on a general difference scheme defined by an [...]

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• 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 [...]

  • 70
  •  read