Reaction–diffusion–convection equations in two spatial dimensions; continuous and discrete dynamics

2021 ◽  
pp. 2150186
Author(s):  
A. S. Carstea
Keyword(s):  
Reaction Diffusion ◽  
Auxiliary Function ◽  
Discrete Dynamics ◽  
Two Dimensional ◽  
Independent Variables ◽  
Nonlinear Reaction ◽  
Spatial Dimensions ◽  
Spatio Temporal ◽  
Diffusion Convection ◽  
Hirota Bilinear

In this paper, we investigate some two-dimensional (with respect to spatial independent variables) reaction–diffusion–convection equations with various nonlinear (reaction) terms. Using Hirota bilinear formalism with a free auxiliary function, we obtain kink solutions and many spatio-temporal discretizations having birational form.

scholarly journals A three‐level time‐split MacCormack method for two‐dimensional nonlinear reaction‐diffusion equations

2020 ◽  
Vol 92 (12) ◽  
pp. 1681-1706 ◽  
Author(s):  
Eric Ngondiep ◽  
Nabil Kerdid ◽  
Mohammed Abdulaziz Mohammed Abaoud ◽  
Ibrahim Abdulaziz Ibrahim Aldayel
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Nonlinear Reaction ◽  
Maccormack Method

Symmetries, ansätze and exact solutions of nonlinear second-order evolution equations with convection terms, II

2006 ◽  
Vol 17 (5) ◽  
pp. 597-605 ◽  
Author(s):  
ROMAN CHERNIHA ◽  
MYKOLA SEROV
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Applied Mathematics ◽  
Reaction Diffusion ◽  
Second Order ◽  
Lie Symmetries ◽  
Nonlinear Reaction ◽  
Diffusion Convection ◽  
Natural Way

New results concerning Lie symmetries of nonlinear reaction-diffusion-convection equations, which supplement in a natural way the results published in the European Journal of Applied Mathematics (9(1998) 527–542) are presented.

scholarly journals Residual power series method for solving nonlinear reaction-diffusion-convection problems

2021 ◽  
Vol 39 (3) ◽  
pp. 177-188
Author(s):  
Maisa Khader ◽  
Mahmoud H. DarAssi
Keyword(s):  
Power Series ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Nonlinear Reaction ◽  
Residual Power Series ◽  
Diffusion Convection ◽  
Residual Power

In this paper, the residual power series method (RPSM) is applied to one of the most frequently used models in engineering and science, a nonlinear reaction diffusion convection initial value problems. The approximate solutions using the RPSM were compared to the exact solutions and to the approximate solutions using the homotopy analysis method.

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