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.

scholarly journals Efficient homotopy perturbation method for fractional non-linear equations using Sumudu transform

2015 ◽  
Vol 19 (4) ◽  
pp. 1167-1171 ◽  
Author(s):  
Ming-Feng Zhang ◽  
Yan-Qin Liu ◽  
Xiao-Shuang Zhou
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Linear Equations ◽  
Solution Process ◽  
Homotopy Perturbation ◽  
Non Linear ◽  
Sumudu Transform ◽  
Non Linear Equations

In this paper, we propose an efficient modification of the homotopy perturbation method for solving fractional non-linear equations with fractional initial conditions. Sumudu transform is adopted to simplify the solution process. An example is given to illustrate the solution process and effectiveness of the method.

scholarly journals An Efficient Two-Step Iterative Technique for Solving Non-Linear Equations

2021 ◽  
pp. 497-509
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Linear Equations ◽  
Test Problems ◽  
Iterative Technique ◽  
Validity And Reliability ◽  
Homotopy Perturbation ◽  
Iterative System ◽  
Non Linear ◽  
Non Linear Equations

We use the homotopy perturbation method (HPM) to construct a new iterative system for solving non-linear equations in this article. The criteria for convergence in the scheme developed are also imposed. To show the validity and reliability of our process, we compare our regime with other current procedures by looking at various test problems.

Optimal control homotopy perturbation method for cancer model

2019 ◽  
Vol 12 (03) ◽  
pp. 1950027 ◽  
Author(s):  
Malihe Najafi ◽  
Hadi Basirzadeh
Keyword(s):  
Mathematical Modeling ◽  
Optimal Control ◽  
Perturbation Method ◽  
Cancer Immunotherapy ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Cancer Model ◽  
Homotopy Perturbation

In this paper, we introduced the optimal control homotopy perturbation method (OCHPM) by using the homotopy perturbation method (HPM). Every one, by using of the proposed method, can obtain numerical solutions of mathematical modeling for cancer-immunotherapy. In this paper, in order to prove the preciseness and efficiency of the OCHPM method, we compared the obtained numerical solutions with HPM. The results obtained showed that the OCHPM method is powerful to generate the numerical solutions for some therapeutic models.

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