Stability and convergence of the difference methods for the space–time fractional advection–diffusion equation

2007 ◽  
Vol 191 (1) ◽  
pp. 12-20 ◽  
Author(s):  
F. Liu ◽  
P. Zhuang ◽  
V. Anh ◽  
I. Turner ◽  
K. Burrage
Keyword(s):  
Diffusion Equation ◽  
Space Time ◽  
Stability And Convergence ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Difference Methods ◽  
The Difference

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.

Implicit Difference Scheme of the Space-Time Fractional Advection Diffusion Equation

2015 ◽  
Vol 18 (6) ◽  
Author(s):  
E. A. Abdel-Rehim
Keyword(s):  
Difference Scheme ◽  
Space Time ◽  
Implicit Difference Scheme ◽  
Approximation Solution ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Long Run ◽  
Pseudo Differential Equation ◽  
The Difference ◽  
Fractional Orders

AbstractThe space-time fractional advection diffusion equations are linear partial pseudo-differential equation with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. We use the implicit difference scheme, the theta-method, to find the approximation solution of these equations in the long run. The proofs of stability of the difference scheme of each models are given. We compare the numerical results of these models for different values of the space and the time fractional orders and for different values of theta.

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