Exact and numerical stability analysis of reaction-diffusion equations with distributed delays

2015 ◽  
Vol 11 (1) ◽  
pp. 189-205 ◽  
Author(s):  
Gengen Zhang ◽  
Aiguo Xiao
Keyword(s):  
Stability Analysis ◽  
Numerical Stability ◽  
Reaction Diffusion ◽  
Distributed Delays ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Numerical Stability Analysis

scholarly journals On the Issue of Radiation-Induced Instability in Binary Solid Solutions

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Santosh Dubey ◽  
S. K. Joshi ◽  
B. S. Tewari
Keyword(s):  
Solid Solution ◽  
Stability Analysis ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Control Parameters ◽  
Binary Solid Solution ◽  
Nonlinear Reaction ◽  
Radiation Induced ◽  
The Stability

The stability of a binary solid solution under irradiation has been studied. This has been done by performing linear stability analysis of a set of nonlinear reaction-diffusion equations under uniform irradiation. Owing to the complexity of the resulting system of eigenvalue equations, a numerical solution has been attempted to calculate the dispersion relations. The set of reaction-diffusion equations represent the coupled dynamics of vacancies, dumbbell-type interstitials, and lattice atoms. For a miscible system (Cu-Au) under uniform irradiation, the initiation and growth of the instability have been studied as a function of various control parameters.

A Revisit of the Semi-Adaptive Method for Singular Degenerate Reaction-Diffusion Equations

2012 ◽  
Vol 2 (3) ◽  
pp. 185-203 ◽  
Author(s):  
Qin Sheng ◽  
A. Q. M. Khaliq
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Stability ◽  
Numerical Experiments ◽  
Reaction Diffusion ◽  
Adaptive Method ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Key Characteristics

AbstractThis article discusses key characteristics of a semi-adaptive finite difference method for solving singular degenerate reaction-diffusion equations. Numerical stability, monotonicity, and convergence are investigated. Numerical experiments illustrate the discussion. The study reconfirms and improves several of our earlier results.

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