A Modified Homotopy Perturbation Method and the Axial Secular Frequencies of a Non-Linear Ion Trap

2012 ◽  
Vol 18 (1) ◽  
pp. 37-42 ◽  
Author(s):  
Alireza Doroudi
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Ion Trap ◽  
Linear Ion Trap ◽  
Homotopy Perturbation ◽  
Non Linear

scholarly journals Mathematical Modeling of Microbial Fuel Cells in Wastewater Treatment - Homotopy Perturbation Method

2019 ◽  
Vol 8 (4) ◽  
pp. 5634-5640
Keyword(s):  
Mathematical Modeling ◽  
Perturbation Method ◽  
Microbial Fuel Cells ◽  
Homotopy Perturbation Method ◽  
Linear Equations ◽  
Rate Equations ◽  
Operating Modes ◽  
Homotopy Perturbation ◽  
Non Linear ◽  
Experimental Values

Mathematical modeling of Microbial Fuel Cell (MFC), which accounts for the co-existence of methanogenic and anodophilic microbial populations for different operating modes and reactor configurations, is discussed. This model based on the system of non-linear rate equations, where the non-linear term is related to the rate of the reactions. The system of non-linear equations is solved by using homotopy perturbation method. In this paper closed form of analytical expression of the concentration of substrate, anodophilic, methanogenic, and the mediator is derived. The analytical expressions are compared with simulation results for the experimental values of parameters, and satisfactory agreement is noted. The influence of parameters on the concentration profiles are discussed.

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