Coupled reaction-diffusion waves in an isothermal autocatalytic chemical system

1993 ◽  
Vol 50 (1) ◽  
pp. 43-76 ◽  
Author(s):  
J. H. MERKIN ◽  
D. J. NEEDHAM ◽  
S. K. SCOTT
Keyword(s):  
Reaction Diffusion ◽  
Chemical System ◽  
Diffusion Waves ◽  
Coupled Reaction

scholarly journals Coupled reaction-diffusion waves in a chemical system via fractional derivatives in Liouville-Caputo sense

2018 ◽  
Vol 64 (5) ◽  
pp. 539 ◽  
Author(s):  
Francisco Gomez ◽  
Khaled Saad
Keyword(s):  
Fractional Derivatives ◽  
Error Function ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Chemical System ◽  
Transform Method ◽  
Diffusion Waves ◽  
Homotopy Analysis ◽  
Optimal Values ◽  
Coupled Reaction

In this paper, we have generalized the fractional cubic isothermal auto-catalytic chemical system (FCIACS) with Liouville-Caputo, Caputo-Fabrizio-Caputo, and Atangana-Baleanu-Caputo fractional time derivatives, respectively. We apply the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of FCIACS using these fractional derivatives. We study the convergence analysis of HATM by computing the residual error function. Also, we find the optimal values of h so we assure the convergence of the approximate solutions. Finally we show the behavior of the approximate solutions graphically. The results obtained are very effectiveness and accuracy.

The development of travelling waves in a simple isothermal chemical system. IV. Quadratic autocatalysis with quadratic decay

1991 ◽  
Vol 434 (1892) ◽  
pp. 531-554 ◽  
Keyword(s):  
Travelling Waves ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Chemical System ◽  
Governing Equations ◽  
Initial Value ◽  
Dimensional Parameter ◽  
Diffusion Waves ◽  
Permanent Form ◽  
Bounds On The Solution

The initiation of travelling reaction-diffusion waves in the chemical system governed by the quadratic autocatalytic or branching reaction A + B → 2B (rate k 1 ab) coupled with the decay or termination step B + B → C (rate k 4 b 2 ) is discussed. The system is described by the non-dimensional parameter K - k 4 / k 1 and parameters representing the local initial input of B. It is shown that a travelling wave of permanent form will develop for all K (and no matter how small the initial input of B). Bounds on the solution of the initial-value problem are obtained as well as numerical integrations of the governing equations. The structure of the permanent form travelling waves that arise is discussed in some detail, as well as the asymptotic limits K → 0 and K → ∞. The behaviour of the solution for this problem is compared with solutions found previously for other related simple autocatalytic systems with autocatalyst decay.

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