Bibliographic citations
Gonzales, M., (2023). Solución numérica de la ecuación de difusión fraccionaria en el tiempo con condiciones de frontera mixtas usando diferencias finitas miméticas [Universidad Nacional de Trujillo]. https://hdl.handle.net/20.500.14414/20487
Gonzales, M., Solución numérica de la ecuación de difusión fraccionaria en el tiempo con condiciones de frontera mixtas usando diferencias finitas miméticas []. PE: Universidad Nacional de Trujillo; 2023. https://hdl.handle.net/20.500.14414/20487
@phdthesis{renati/1045803,
title = "Solución numérica de la ecuación de difusión fraccionaria en el tiempo con condiciones de frontera mixtas usando diferencias finitas miméticas",
author = "Gonzales Herrera, Mardo Victor",
publisher = "Universidad Nacional de Trujillo",
year = "2023"
}
In this thesis, a new numerical scheme is described that solves the fractional diffusion equation in time with mixed boundary conditions, which combines the implicit finite difference method, used to discretize the Caputo fractional derivative of the temporal variable, and the mimetic finite difference method, used to discretize the second order differential operator of the spatial variable, including the boundary conditions. Replacing the diffusion equation of fractional order in time, by a system of discrete algebraic equations that iteratively associate the first two midpoints closest to the boundary, as well as for the interior points of the discrete domain, results in an unconditionally stable scheme. Using the Von Neumann criterion on the iterative formulas for the right and left boundaries as well as for the strictly interior points of the discrete domain,is obtained a convergence of order O ( 2 + h2), where 0 < < 1. The computational experiments obtained using the maximum norm show the efficiency and goodness of the proposed numerical method, unlike the implicit finite difference method as a consequence of the mimetic discretization for different step lengths in time ( t) and different instances of time.
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