scholarly journals A higher-order compact ADI method with monotone iterative procedure for systems of reaction–diffusion equations

2011 ◽  
Vol 62 (6) ◽  
pp. 2434-2451 ◽  
Author(s):  
Yuan-Ming Wang ◽  
Jie Wang
Keyword(s):  
Iterative Procedure ◽  
Reaction Diffusion ◽  
Higher Order ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Adi Method ◽  
Monotone Iterative

Attractors with higher-order regularity of stochastic reaction–diffusion equations on time-varying domains

2020 ◽  
Vol 20 (02) ◽  
pp. 2050041
Author(s):  
Lu Yang ◽  
Meihua Yang ◽  
Peter Kloeden
Keyword(s):  
Reaction Diffusion ◽  
Higher Order ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Initial Time ◽  
Regular Space ◽  
Time Varying ◽  
Regularity Properties ◽  
Random Attractors ◽  
Stochastic Reaction

Random attractors and their higher-order regularity properties are studied for stochastic reaction–diffusion equations on time-varying domains. Some new a priori estimates for the difference of solutions near the initial time and the continuous dependence in initial data in [Formula: see text] are proved. Then attraction of the random attractors in the higher integrability space [Formula: see text] for any [Formula: see text] and the regular space [Formula: see text] is established.

scholarly journals An ADI Method for the Numerical Solution of 3D Fractional Reaction-Diffusion Equations

2020 ◽  
Vol 4 (4) ◽  
pp. 57
Author(s):  
Moreno Concezzi ◽  
Renato Spigler
Keyword(s):  
Fluid Flows ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Three Dimensions ◽  
Diffusion Equations ◽  
Diffusion Type ◽  
Pagerank Algorithm ◽  
Adi Method ◽  
Alternating Direction ◽  
Flows Through Porous Media

A numerical method for solving fractional partial differential equations (fPDEs) of the diffusion and reaction–diffusion type, subject to Dirichlet boundary data, in three dimensions is developed. Such fPDEs may describe fluid flows through porous media better than classical diffusion equations. This is a new, fractional version of the Alternating Direction Implicit (ADI) method, where the source term is balanced, in that its effect is split in the three space directions, and it may be relevant, especially in the case of anisotropy. The method is unconditionally stable, second-order in space, and third-order in time. A strategy is devised in order to improve its speed of convergence by means of an extrapolation method that is coupled to the PageRank algorithm. Some numerical examples are given.

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