scholarly journals Application of operator splitting to solve reaction-diffusion equations

2012 ◽  
Author(s):  
Tamás Ladics
Keyword(s):  
Operator Splitting ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations

scholarly journals Splitting spectral element method for fractional reaction-diffusion equations

2020 ◽  
Vol 14 ◽  
pp. 174830262096670
Author(s):  
Qi Li ◽  
Fangying Song
Keyword(s):  
Spectral Element Method ◽  
Operator Splitting ◽  
Reaction Diffusion ◽  
Spectral Element ◽  
Second Order ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Nonlinear Solver ◽  
Fractional Reaction ◽  
Element Method

In this paper, we propose a second-order operator splitting spectral element method for solving fractional reaction-diffusion equations. In order to achieve a fast second-order scheme in time, we decompose the original equation into linear and nonlinear sub-equations, and combine a quarter-time nonlinear solver and a half-time linear solver followed by final quarter-time nonlinear solver. The spatial discretization is eigen-decomposition based on spectral element method. Since this method gives a full diagonal representation of the fractional operator and gets an exponential convergence in space. We have an accurate and efficient approach for solving spacial fractional reaction-diffusion equations. Some numerical experiments are carried out to demonstrate the accuracy and efficiency of this method. Finally, we apply the proposed method to investigate the effect of the fractional order in the fractional reaction-diffusion equations.

scholarly journals Analysis of Operator Splitting in the Nonasymptotic Regime for Nonlinear Reaction-Diffusion Equations. Application to the Dynamics of Premixed Flames

2014 ◽  
Vol 52 (3) ◽  
pp. 1311-1334 ◽  
Author(s):  
Stéphane Descombes ◽  
Max Duarte ◽  
Thierry Dumont ◽  
Frédérique Laurent ◽  
Violaine Louvet ◽  
...  
Keyword(s):  
Operator Splitting ◽  
Premixed Flames ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Nonlinear Reaction

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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