Heterogeneous removal of one or more chain-carrying species at first explosion limit of hydrogen + oxygen mixtures. Part 2.—An analytical solution of the diffusion equations

1968 ◽  
Vol 64 (0) ◽  
pp. 1589-1602
Author(s):  
D. R. Clark ◽  
R. F. Simmons ◽  
D. R. Blackmore
Keyword(s):  
Analytical Solution ◽  
Diffusion Equations ◽  
Explosion Limit

An analytical solution of multi-dimensional space fractional diffusion equations with variable coefficients

2020 ◽  
pp. 2150006
Author(s):  
Pratibha Verma ◽  
Manoj Kumar
Keyword(s):  
Analytical Solution ◽  
Diffusion Coefficients ◽  
High Efficiency ◽  
Dimensional Space ◽  
Adomian Decomposition Method ◽  
Fractional Diffusion ◽  
Variable Coefficients ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
Adomian Decomposition

In this paper, we have considered the multi-dimensional space fractional diffusion equations with variable coefficients. The fractional operators (derivative/integral) are used based on the Caputo definition. This study provides an analytical approach to determine the analytical solution of the considered problems with the help of the two-step Adomian decomposition method (TSADM). Moreover, new results have been obtained for the existence and uniqueness of a solution by using the Banach contraction principle and a fixed point theorem. We have extended the dimension of the space fractional diffusion equations with variable coefficients into multi-dimensions. Finally, the generalized problems with two different types of the forcing term have been included demonstrating the applicability and high efficiency of the TSADM in comparison to other existing numerical methods. The diffusion coefficients do not require to satisfy any certain conditions/restrictions for using the TSADM. There are no restrictions imposed on the problems for diffusion coefficients, and a similar procedures of the TSADM has followed to the obtained analytical solution for the multi-dimensional space fractional diffusion equations with variable coefficients.

scholarly journals APPROXIMATE ANALYTICAL SOLUTION FOR NON-LINEAR REACTION DIFFUSION EQUATIONS IN MODELING OF A BACTERIAL AND FUNGAL BIOFILTER

2020 ◽  
pp. 59-71
Author(s):  
K. M. DHARMALINGAM ◽  
K. VALLI ◽  
M. VEERAMUNI
Keyword(s):  
Mathematical Modeling ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Inversion Method ◽  
Linear Reaction ◽  
Analytical Result ◽  
Fungal Biofilter

The aim of the present work is to find the solution for concentration of pollutant in the biofilm phase using HPM with complex inversion method. The obtained results are validated and illustrate the efficiency of future technique from the figure. Furthermore, the reported analytical result is useful in future modification of mathematical modeling of the biofilter.

Sign in / Sign up

Export Citation Format

Share Document