scholarly journals Traveling Waves for a Bistable Reaction-Diffusion Equation with Delay

2018 ◽  
Vol 50 (1) ◽  
pp. 1175-1199 ◽  
Author(s):  
Sergei Trofimchuk ◽  
Vitaly Volpert
Keyword(s):  
Diffusion Equation ◽  
Traveling Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Equation With Delay

scholarly journals Linear θ-Method and Compact θ-Method for Generalised Reaction-Diffusion Equation with Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Fengyan Wu ◽  
Qiong Wang ◽  
Xiujun Cheng ◽  
Xiaoli Chen
Keyword(s):  
Diffusion Equation ◽  
Necessary Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Stability And Convergence ◽  
Asymptotically Stable ◽  
Sufficient And Necessary Conditions ◽  
Equation Solvability ◽  
Equation With Delay ◽  
Theoretical Results

This paper is concerned with the analysis of the linear θ-method and compact θ-method for solving delay reaction-diffusion equation. Solvability, consistence, stability, and convergence of the two methods are studied. When θ∈[0,1/2), sufficient and necessary conditions are given to show that the two methods are asymptotically stable. When θ∈[1/2,1], the two methods are proven to be unconditionally asymptotically stable. Finally, several examples are carried out to confirm the theoretical results.

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