Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space–time fractional advection-diffusion equation

2020 ◽  
Author(s):  
H. Safdari ◽  
Y. Esmaeelzade Aghdam ◽  
J. F. Gómez-Aguilar
Keyword(s):  
Diffusion Equation ◽  
Convergence Analysis ◽  
Space Time ◽  
Chebyshev Collocation ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Fourth Kind

Space-Time and Motion to Advection-Diffusion Equation

2021 ◽  
Vol 3 (1) ◽  
pp. 34-43
Author(s):  
Mohammad Ghani
Keyword(s):  
Diffusion Equation ◽  
Space Time ◽  
Numerical Results ◽  
Smooth Functions ◽  
Equation Problem ◽  
Time Motion ◽  
Advection Diffusion Equation ◽  
Time And Motion ◽  
Advection Diffusion ◽  
Finite Differences Method

AbstractWe are concerned with the study the differential equation problem of space-time and motion for the case of advection-diffusion equation. We derive the advection-diffusion equation from the conservation of mass, where this can be represented by the substance flow in and flow out through the medium. In this case, the concentration of substance and rate of flow of substance in a medium are smooth functions which is useful to generate advection-diffusion equation. A special case of the advection-diffusion equation and numerical results are also given in this paper. We use explicit and implicit finite differences method for numerical results implemented in MATLAB.Keywords: advection-diffusion; space-time; motion; finite difference method. AbstrakKami tertarik untuk mempelajari masalah persamaan diferensial ruang-waktu, dan gerak untuk kasus persamaan adveksi-difusi. Kita menurunkan persamaan adveksi-difusi dari kekekalan massa, di mana hal ini dapat diwakili oleh aliran zat yang masuk dan keluar melalui media. Dalam hal ini konsentrasi zat dan laju aliran zat dalam suatu medium merupakan fungsi halus yang berguna untuk menghasilkan persamaan adveksi-difusi. Sebuah kasus khusus persamaan adveksi-difusi dan hasil numerik juga diberikan dalam makalah ini. Kami menggunakan metode beda hingga explisit dan implisit untuk hasil numerik yang diimplementasikan dalam MATLAB.Kata kunci: adveksi-difusi; ruang-waktu; gerak; metode beda hingga.

ANÁLISE DE CONVERGÊNCIA DO MÉTODO GILTT PARA PROBLEMAS EM DISPERSÃO DE POLUENTES NA ATMOSFERA

2016 ◽  
Vol 38 ◽  
pp. 182 ◽  
Author(s):  
Daniela Buske ◽  
Cláudio Zen Petersen ◽  
Régis Sperotto de Quadros ◽  
Glênio Aguiar Gonçalves ◽  
Juliana Ávila Contreira
Keyword(s):  
Diffusion Equation ◽  
Convergence Analysis ◽  
Existence And Uniqueness ◽  
Analytic Solution ◽  
Pollutant Dispersion ◽  
Analytical Representation ◽  
Multidimensional Case ◽  
The Past ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

In this paper, we present a convergence analysis of the GILTT method for pollutant dispersion problems consolidating the solution of the problem in analytical representation. There have been many advances in the GILTT technique over the past few years. The advection-diffusion equation was solved for the multidimensional case and applied to various situations, mainly in pollutant dispersion. The theorem of Cauchy-Kowalewsky guarantees the existence and uniqueness of an analytic solution for the advection-diffusion equation. In this paper, we present a convergence analysis for the GILTT method to pollutant dispersion problems. Numerical results are presented.

scholarly journals Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation

Entropy ◽  
2017 ◽  
Vol 19 (7) ◽  
pp. 297 ◽  
Author(s):  
Yuriy Povstenko ◽  
Tamara Kyrylych
Keyword(s):  
Diffusion Equation ◽  
Space Time ◽  
Advection Diffusion Equation ◽  
Advection Diffusion
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