Open Access

ARTICLE

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

Gerardo Tinoco-Guerrero^1,2, Francisco Javier Domínguez Mota^1,3, José Alberto Guzmán Torres¹, José Gerardo Tinoco-Ruiz¹

1 Universidad Michoacana de San Nicolás de Hidalgo
2 Universidad Vasco de Quiroga
3 Aulas CIMNE Network

* Corresponding Authors: Gerardo Tinoco-Guerrero (), Francisco Javier Domínguez Mota (), José Alberto Guzmán Torres (), José Gerardo Tinoco-Ruiz ()

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 2022, 38(2), 1-14. https://doi.org/10.23967/j.rimni.2022.06.003

Received 20 September 2021; Accepted 08 June 2022; Issue published 14 June 2022

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.

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Keywords

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