Controlled Picard Method for Solving Nonlinear Fractional Reaction–Diffusion Models in Porous Catalysts

2017 ◽  
Vol 204 (6) ◽  
pp. 635-647 ◽  
Author(s):  
Mourad S. Semary ◽  
Hany N. Hassan ◽  
Ahmed G. Radwan
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Models ◽  
Porous Catalysts ◽  
Picard Method ◽  
Fractional Reaction

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

scholarly journals The interplay between phenotypic and ontogenetic plasticities can be assessed using reaction-diffusion models

2017 ◽  
Vol 43 (2) ◽  
pp. 247-264 ◽  
Author(s):  
Aldo Ledesma-Durán ◽  
Lorenzo-Héctor Juárez-Valencia ◽  
Juan-Bibiano Morales-Malacara ◽  
Iván Santamaría-Holek
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Models

scholarly journals Approximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji’s Methods

2021 ◽  
Vol 8 (4) ◽  
pp. 527-537
Author(s):  
Ramu UshaRani ◽  
Lakshmanan Rajendran ◽  
Marwan Abukhaled
Keyword(s):  
Taylor Series ◽  
Arbitrary Shape ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Effectiveness Factor ◽  
Michaelis Constant ◽  
Thiele Modulus ◽  
Porous Catalysts ◽  
Analytical Approaches ◽  
Analytical Expressions

A mathematical model of reaction-diffusion problem with Michaelis-Menten kinetics in catalyst particles of arbitrary shape is investigated. Analytical expressions of the concentration of substrates are derived as functions of the Thiele modulus, the modified Sherwood number, and the Michaelis constant. A Taylor series approach and the Akbari-Ganji's method are utilized to determine the substrate concentration and the effectiveness factor. The effects of the shape factor on the concentration profiles and the effectiveness factor are discussed. In addition to their simple implementations, the proposed analytical approaches are reliable and highly accurate, as it will be shown when compared with numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document