High-accuracy numerical scheme for solving the space-time fractional advection-diffusion equation with convergence analysis

This paper presents numerical simulation of one-dimensional advection-diffusion equation. We study the analytical solution of advection diffusion equation as an initial value problem in infinite space and realize the qualitative behavior of the solution in terms of advection and diffusion co-efficient. We obtain the numerical solution of this equation by using explicit centered difference scheme and Crank-Nicolson scheme for prescribed initial and boundary data. We implement the numerical scheme by developing a computer programming code and present the stability analysis of Crank-Nicolson scheme for ADE. For the validity test, we perform error estimation of the numerical scheme and presented the numerical features of rate of convergence graphically. The qualitative behavior of the ADE for different choice of the advection and diffusion co-efficient is verified. Finally, we estimate the pollutant in a river at different times and different points by using these numerical scheme. Bangladesh J. Sci. Ind. Res.55(1), 15-22, 2020

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An unconditionally stable algorithm for multiterm time fractional advection–diffusion equation with variable coefficients and convergence analysis

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22629 ◽

2020 ◽

Author(s):

Adivi Sri Venkata Ravi Kanth ◽

Neetu Garg

Keyword(s):

Diffusion Equation ◽

Convergence Analysis ◽

Variable Coefficients ◽

Unconditionally Stable ◽

Stable Algorithm ◽

Advection Diffusion Equation ◽

Advection Diffusion

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Space-Time and Motion to Advection-Diffusion Equation

InPrime: Indonesian Journal of Pure and Applied Mathematics ◽

10.15408/inprime.v3i1.19679 ◽

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.

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

Ciência e Natura ◽

10.5902/2179460x20156 ◽

2016 ◽

Vol 38 ◽

pp. 182 ◽

Cited By ~ 1

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.

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