scholarly journals Analysis of Biodegradation and Microbial Growth in Groundwater System Using New the Homotopy Perturbation Method

2021 ◽  
Vol 12 (1S) ◽  
pp. 606-614
Author(s):  
S. Thamizh Suganya, Et. al.
Keyword(s):  
Perturbation Method ◽  
Microbial Growth ◽  
Homotopy Perturbation Method ◽  
Monod Kinetics ◽  
Approximate Analytical Expression ◽  
Groundwater System ◽  
Homotopy Perturbation ◽  
Cell Counts ◽  
Direct Cell ◽  
Linear Differential

In this paper, we drive the concentration of microbial growth in the groundwater system. This model is based on the system of non-linear differential equations. The system of equations is solved by using the new homotopy perturbation method. We followed toluene degradation and bacterial growth by measuring toluene and oxygen concentrations and by direct cell counts. And the total amount of toluene degraded by Pseudomonal putida F1 in the sediment columns increased with rising concentration of the source and flow rate. In contrast, the efficiency of toluene removal slowly decreases. The approximate analytical expression of this model, the concentration of toluene and bacteria also consideration of a metabolite concentration, the microbial growth of attached and suspended bacteria, depending on the simultaneous presence of toluene. Finally, oxygen and dual Monod kinetics are discussed. The analytical solutions are also compared with simulation results and satisfactory the agreement is noted.

scholarly journals Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations

2017 ◽  
Vol 21 (4) ◽  
pp. 1843-1846 ◽  
Author(s):  
Zhen-Jiang Liu ◽  
Magaji Adamu ◽  
Enoch Suleiman ◽  
Ji-Huan He
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Laplace Transformation ◽  
Homotopy Perturbation Method ◽  
Solution Process ◽  
Initial Approximation ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Linear Differential

Homotopy perturbation method is combined with Laplace transformation to obtain approximate analytical solutions of non-linear differential equations. An example is given to elucidate the solution process and confirm reliability of the method. The result indicates superiority of the method over the conventional homotopy perturbation method due its flexibility in choosing its initial approximation.

Application of New Homotopy Perturbation Method for Solving Partial Differential Equations

2018 ◽  
Vol 15 (2) ◽  
pp. 500-508 ◽  
Author(s):  
Musa R. Gad-Allah ◽  
Tarig M. Elzaki
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Novel Technique ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear Differential

In this paper, a novel technique, that is to read, the New Homotopy Perturbation Method (NHPM) is utilized for solving a linear and non-linear differential equations and integral equations. The two most important steps in the application of the new homotopy perturbation method are to invent a suitable homotopy equation and to choose a suitable initial conditions. Comparing between the effects of the method (NHPM), is given exact solution, and the method (HPM), is given approximate solution, in this paper, we make some instances are provided to prove the ability of the method (NHPM). Show that the method (NHPM) is valid and effective, easy and accurate in solving linear and nonlinear differential equations, compared with the Homotopy Perturbation Method (HPM).

scholarly journals UNSTEADY SQUEEZING FLOW OF A VISCOUS MHD FLUID BETWEEN PARALLEL PLATES, A SOLUTION USING THE HOMOTOPY PERTURBATION METHOD

2008 ◽  
Vol 13 (4) ◽  
pp. 565-576 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Sania Irum ◽  
Ali R. Ansari
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Similarity Transformation ◽  
Squeezing Flow ◽  
Total Resistance ◽  
Parallel Plates ◽  
Homotopy Perturbation ◽  
Linear Differential ◽  
The Magnetic Field ◽  
Range Of Values

The present paper analyses the unsteady 2‐dimensional flow of a viscous MHD fluid between two parallel infinite plates. The two infinite plates are considered to be approaching each other symmetrically, causing the squeezing flow. A similarity transformation is used to reduce the partial differential equations modeling the flow, to a single fourth‐order non‐linear differential equation containing the Reynolds number and the magnetic field strength as parameters. The velocity functions are obtained for a range of values of both parameters by using the homotopy perturbation method. The total resistance to the upper plate is presented.

scholarly journals Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2215
Author(s):  
Haji Gul ◽  
Sajjad Ali ◽  
Kamal Shah ◽  
Shakoor Muhammad ◽  
Thanin Sitthiwirattham ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Order Partial Differential Equation ◽  
Two Dimensional ◽  
Numerical Treatment ◽  
Helmholtz Equations ◽  
Homotopy Perturbation ◽  
Linear Differential

In this article, we introduce a new algorithm-based scheme titled asymptotic homotopy perturbation method (AHPM) for simulation purposes of non-linear and linear differential equations of non-integer and integer orders. AHPM is extended for numerical treatment to the approximate solution of one of the important fractional-order two-dimensional Helmholtz equations and some of its cases . For probation and illustrative purposes, we have compared the AHPM solutions to the solutions from another existing method as well as the exact solutions of the considered problems. Moreover, it is observed that the symmetry or asymmetry of the solution of considered problems is invariant under the homotopy definition. Error estimates for solutions are also provided. The approximate solutions of AHPM are tabulated and plotted, which indicates that AHPM is effective and explicit.

scholarly journals The study of heat transfer phenomena by using modified homotopy perturbation method coupled by Laplace transform

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1105-1115
Author(s):  
Uriel Filobello-Nino ◽  
Hector Vazquez-Leal ◽  
Agustin Herrera-May ◽  
Roberto Ambrosio-Lazaro ◽  
Victor Jimenez-Fernandez ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Non Linear ◽  
Linear Problems ◽  
Linear Differential

In this paper, we present modified homotopy perturbation method coupled by Laplace transform to solve non-linear problems. As case study modified homotopy perturbation method coupled by Laplace transform is employed in order to obtain an approximate solution for the non-linear differential equation that describes the steady-state of a heat 1-D flow. The comparison between approximate and exact solutions shows the practical potentiality of the method.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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