Numerical experiments with an adaptive model of a marine ecosystem represented by the reaction-diffusion equations

2012 ◽  
Vol 21 (6) ◽  
pp. 424-436
Author(s):  
E. V. Romanovskii ◽  
I. E. Timchenko
Keyword(s):  
Numerical Experiments ◽  
Marine Ecosystem ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Adaptive Model

scholarly journals Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Dongfang Li ◽  
Chao Tong ◽  
Jinming Wen
Keyword(s):  
Numerical Experiments ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Variable Delay ◽  
Discrete Energy ◽  
Continuous Problems ◽  
Rate Of Decay ◽  
The Stability ◽  
Theoretical Results

This paper is concerned with the stability of non-Fickian reaction-diffusion equations with a variable delay. It is shown that the perturbation of the energy function of the continuous problems decays exponentially, which provides a more accurate and convenient way to express the rate of decay of energy. Then, we prove that the proposed numerical methods are sufficient to preserve energy stability of the continuous problems. We end the paper with some numerical experiments on a biological model to confirm the theoretical results.

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.

An Improved Error Estimate for a Numerical Method for a System of Coupled Singularly Perturbed Reaction-diffusion Equations

2003 ◽  
Vol 3 (3) ◽  
pp. 417-423 ◽  
Author(s):  
Torsten Linss ◽  
Niall Madden
Keyword(s):  
Numerical Experiments ◽  
Reaction Diffusion ◽  
Perturbation Parameter ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Central Difference ◽  
Central Difference Scheme ◽  
Coupled Reaction ◽  
Theoretical Results

AbstractWe consider a central difference scheme for the numerical solution of a system of coupled reaction-diffusion equations. We show that the scheme is almost second-order convergent, uniformly in the perturbation parameter. We present the results of numerical experiments to confirm our theoretical results.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

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