scholarly journals Approximate Solution of Non-Linear Reaction-Diffusion in A Thin Membrane: Taylor Series Method

2021 ◽  
Vol 12 (1S) ◽  
pp. 586-594
Author(s):  
J. Visuvasam, Et. al.
Keyword(s):  
Taylor Series ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Series Method ◽  
Thin Membrane ◽  
Nonlinear Reaction ◽  
Closed Type ◽  
Taylor Series Method ◽  
Exponential Function Method

The nonlinear reaction-diffusion cycle in the thin membrane that describes the chemical reactions involving three species is studied. The model consists of the system of on nonlinear reaction-diffusion equations. The closed type of analytical expression of concentrations for the enzyme was developed by solving equations using the Taylor series formula. This results in the mixed Dirichlet and Neumann boundary conditions. Taylor series method similar to exponential function method. This technique provides approximate and simple solutions that are quick, easy to compute, and efficiently correct. These estimated findings are compared to the nuxmerical results. There is a good agreement with the simulation results.

scholarly journals A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Kanittha Yimnak ◽  
Anirut Luadsong
Keyword(s):  
Interpolation Method ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Kriging Interpolation ◽  
Time Step ◽  
Heaviside Step Function ◽  
Nonlinear Reaction ◽  
Integral Equation Formulation

The meshless local Pretrov-Galerkin method (MLPG) with the test function in view of the Heaviside step function is introduced to solve the system of coupled nonlinear reaction-diffusion equations in two-dimensional spaces subjected to Dirichlet and Neumann boundary conditions on a square domain. Two-field velocities are approximated by moving Kriging (MK) interpolation method for constructing nodal shape function which holds the Kronecker delta property, thereby enhancing the arrangement nodal shape construction accuracy, while the Crank-Nicolson method is chosen for temporal discretization. The nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical examples with investigating the convergence and the accuracy of numerical results. The numerical experiments revealing the solutions by the developed formulation are stable and more precise.

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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