Analysis of the Numerical Solution in the One Dimensional Non-Stationary Diffusion Equation using Schemes of Finite Mimetic Differences and Crank-Nicolson

• Autores: Gonzales Herrera, Mardo, Murillo Cornejo, Saulo
• Formato: artículo
• Fecha de Publicación: 2018
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revista UNITRU - Selecciones Matemáticas
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/1982
• Enlace del recurso: http://revistas.unitru.edu.pe/index.php/SSMM/article/view/1982
• Nivel de acceso: acceso abierto
• Materia: Algorithm in matlab; Mimetic operators; Diffusion equation; Mimetic finite difference method; Crank Nicolson scheme; Algoritmo en matlab; Operadores miméticos; Ecuación de difusión; Método de diferencias finitas miméticas; Esquema Crank-Nicolson

The numerical solution of the one-dimensional non-static diffusion equation is proposed, developing an algorithm in software Matlab version 7.0, for which the mimetic finite difference scheme is combined in the approximation of the differential operators of the continuum (gradient and divergence) for the spatialvariable, on a uniform grid, whose discrete differential operators have a second order approximation and the finite difference approach type Crank Nicolson for approximations in the temporary variable.This proposed algorithm for the mimetic and Crank Nicolson approaches has a better approximation than the finite-difference Crank Nicolson-type scheme.In addition, the approximation error generated between the numerical solution and the analytical solution is calculated using the maximum standard for the non-stationary diffusion equation with Robin type boundary conditions.