Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations – Homotopy perturbation approach

2010 ◽  
Vol 644 (1) ◽  
pp. 50-59 ◽  
Author(s):  
A. Meena ◽  
L. Rajendran
Keyword(s):  
Mathematical Modeling ◽  
Linear Equations ◽  
Perturbation Approach ◽  
Homotopy Perturbation ◽  
Non Linear ◽  
Non Linear Equations

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.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

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