scholarly journals Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

2017 ◽  
Vol 937 ◽  
pp. 012041
Author(s):  
A D Polyanin ◽  
V G Sorokin
Keyword(s):  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Test Problems ◽  
Nonlinear Reaction ◽  
Equations With Delay

scholarly journals On the Long Time Simulation of Reaction-Diffusion Equations with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dongfang Li ◽  
Chengjian Zhang
Keyword(s):  
Numerical Method ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Open Problems ◽  
Time Simulation ◽  
Long Time ◽  
Continuous Problem ◽  
Equations With Delay

For a consistent numerical method to be practically useful, it is widely accepted that it must preserve the asymptotic stability of the original continuous problem. However, in this study, we show that it may lead to unreliable numerical solutions in long time simulation even if a classical numerical method gives a larger stability region than that of the original continuous problem. Some numerical experiments on the reaction-diffusion equations with delay are presented to confirm our findings. Finally, some open problems on the subject are proposed.

Sign in / Sign up

Export Citation Format

Share Document