Numerical Solution of a Two-Dimensional Anomalous Diffusion Problem

2011 ◽  
pp. 249-261
Author(s):  
Necati Özdemir ◽  
Derya Avcı
Keyword(s):  
Numerical Solution ◽  
Anomalous Diffusion ◽  
Diffusion Problem ◽  
Two Dimensional

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

scholarly journals Exact solution and invariant for fractional Cattaneo anomalous diffusion of cells in two-dimensional comb framework

2017 ◽  
Vol 89 (1) ◽  
pp. 213-224 ◽  
Author(s):  
Lin Liu ◽  
Liancun Zheng ◽  
Fawang Liu ◽  
Xinxin Zhang
Keyword(s):  
Exact Solution ◽  
Anomalous Diffusion ◽  
Two Dimensional

scholarly journals Perturbation of eigenvalues due to gaps in two-dimensional boundaries

2006 ◽  
Vol 463 (2079) ◽  
pp. 759-786 ◽  
Author(s):  
Anthony M.J Davis ◽  
Stefan G Llewellyn Smith
Keyword(s):  
Eigenvalue Problems ◽  
Numerical Solutions ◽  
Neumann Boundary ◽  
Diffusion Problem ◽  
Length Scale ◽  
Two Dimensional ◽  
Constructive Approach ◽  
Term Outcome ◽  
Long Term Outcome

Motivated by problems involving diffusion through small gaps, we revisit two-dimensional eigenvalue problems with localized perturbations to Neumann boundary conditions. We recover the known result that the gravest eigenvalue is O (|ln  ϵ | −1 ), where ϵ is the ratio of the size of the hole to the length-scale of the domain, and provide a simple and constructive approach for summing the inverse logarithm terms and obtaining further corrections. Comparisons with numerical solutions obtained for special geometries, both for the Dirichlet ‘patch problem’ where the perturbation to the boundary consists of a different boundary condition and for the gap problem, confirm that this approach is a simple way of obtaining an accurate value for the gravest eigenvalue and hence the long-term outcome of the underlying diffusion problem.

Sign in / Sign up

Export Citation Format

Share Document