Homotopy perturbation method for predicting tsunami wave propagation with crisp and uncertain parameters

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Perumandla Karunakar ◽  
Snehashish Chakraverty
Keyword(s):  
Wave Propagation ◽  
Perturbation Method ◽  
Water Wave ◽  
Design Methodology ◽  
Homotopy Perturbation Method ◽  
Tsunami Wave ◽  
Uncertain Parameters ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Good Agreement

Purpose The purpose of this paper is to find the solution of classical nonlinear shallow-water wave (SWW) equations in particular to the tsunami wave propagation in crisp and interval environment. Design/methodology/approach Homotopy perturbation method (HPM) has been used for handling crisp and uncertain differential equations governing SWW equations. Findings The wave height and depth-averaged velocity of a tsunami wave in crisp and interval cases have been obtained. Originality/value Present results by HPM are compared with the existing solution (in crisp case), and they are found to be in good agreement. Also, the residual error of the solutions is found for the convergence conformation and reliability of the present results.

Homotopy perturbation method for peristaltic motion of gold-blood nanofluid with heat source

2019 ◽  
Vol 30 (6) ◽  
pp. 3121-3138 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Abdulrahman F. Aljohani ◽  
Emad H. Aly
Keyword(s):  
Gold Nanoparticles ◽  
Heat Source ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Human Cancer ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Blood Temperature ◽  
Flow And Heat Transfer ◽  
Diagnosis Therapy

PurposeThis paper aims to investigate the impacts of the gold nanoparticles on the peristaltic flow and heat transfer of blood in the presence of heat source. This element has been chosen because on comparing with the other common nanoparticles, gold nanoparticles are preferred due to their unique properties in absorbing the temperature when a heat source exists.Design/methodology/approachOn simplifying the governing equations under the assumption of long-wavelength and low-Reynolds number approximations, the resulted system has been solved by applying the homotopy perturbation method. Then, detailed physical discussion has been introduced through several plots while focusing on the consequences of the current results on the treatment of cancer.FindingsThe present results revealed that the heat source has a great effect on the blood velocity, blood temperature and concentration of the gold nanoparticles within the artery/vein cavity when represented as asymmetric channel. Moreover, the accuracy of the current solutions was validated through several plots of the remainder error for each studied phenomenon.Originality/valueThe current idea gives some light on the attempts of using the gold nanoparticles in the treatment of cancer and therefore may lead to possible applications for diagnosis/therapy of the human cancer. To the best of authors’ knowledge, this is novel, very efficient and applicable.

Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix

2021 ◽  
Author(s):  
Rachid Belgacem ◽  
Ahmed Bokhari ◽  
Salih Djilali ◽  
Sunil Kumar
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Operational Matrix ◽  
Inversion Method ◽  
Numerical Inversion ◽  
Homotopy Perturbation ◽  
Boubaker Polynomials ◽  
The Laplace Transform ◽  
Good Agreement

We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix. The efficiency of the presented approach is demonstrated by solving some differential equations. Also, this technique is combined with the standard Laplace Homotopy Perturbation Method. The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.

The homotopy perturbation method for fractional differential equations: part 1 Mohand transform

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Nadeem ◽  
Ji-Huan He ◽  
Asad Islam
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Fractional Pdes ◽  
Specific Objective ◽  
Multiple Behaviors ◽  
Fractional Differential ◽  
Positive Integers

Purpose This study aims that very lately, Mohand transform is introduced to solve the ordinary and partial differential equations (PDEs). In this paper, the authors modify this transformation and associate it with a further analytical method called homotopy perturbation method (HPM) for the fractional view of Newell–Whitehead–Segel equation (NWSE). As Mohand transform is restricted to linear obstacles only, as a consequence, HPM is used to crack the nonlinear terms arising in the illustrated problems. The fractional derivatives are taken into the Caputo sense. Design/methodology/approach The specific objective of this study is to examine the problem which performs an efficient role in the form of stripe orders of two dimensional systems. The authors achieve the multiple behaviors and properties of fractional NWSE with different positive integers. Findings The main finding of this paper is to analyze the fractional view of NWSE. The obtain results perform very good in agreement with exact solution. The authors show that this strategy is absolutely very easy and smooth and have no assumption for the constriction of this approach. Research limitations/implications This paper invokes these two main inspirations: first, Mohand transform is associated with HPM, secondly, fractional view of NWSE with different positive integers. Practical implications In this paper, the graph of approximate solution has the excellent promise with the graphs of exact solutions. Social implications This paper presents valuable technique for handling the fractional PDEs without involving any restrictions or hypothesis. Originality/value The authors discuss the fractional view of NWSE by a Mohand transform. The work of the present paper is original and advanced. Significantly, to the best of the authors’ knowledge, no such work has yet been published in the literature.

The homotopy perturbation method for fractional differential equations: part 2, two-scale transform

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Nadeem ◽  
Ji-Huan He
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Differential Equations ◽  
Homotopy Perturbation Method ◽  
Solution Process ◽  
Solid State Physics ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Fractional Differential

Purpose The purpose of this paper is to find an approximate solution of a fractional differential equation. The fractional Newell–Whitehead–Segel equation (FNWSE) is used to elucidate the solution process, which is one of the nonlinear amplitude equation, and it enhances a significant role in the modeling of various physical phenomena arising in fluid mechanics, solid-state physics, optics, plasma physics, dispersion and convection systems. Design/methodology/approach In Part 1, the authors adopted Mohand transform to find the analytical solution of FNWSE. In this part, the authors apply the fractional complex transform (the two-scale transform) to convert the problem into its differential partner, and then they introduce the homotopy perturbation method (HPM) to bring down the nonlinear terms for the approximate solution. Findings The HPM makes numerical simulation for the fractional differential equations easy, and the two-scale transform is a strong tool for fractal models. Originality/value The HPM with the two-scale transform sheds a bright light on numerical approach to fractional calculus.

scholarly journals Homotopy perturbation method for a Stefan problem with variable latent heat

2014 ◽  
Vol 18 (2) ◽  
pp. 391-398 ◽  
Author(s):  
R Rajeev
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Perturbation Method ◽  
Latent Heat ◽  
Stefan Problem ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Variable Latent Heat ◽  
Good Agreement

In this paper, homotopy perturbation method is successfully applied to find an approximate solution of one phase Stefan problem with variable latent heat. The results thus obtained are compared graphically with a published analytical solution and are in good agreement.

Investigation of Casimir and Van der Waals Forces for a Nonlinear Double-Clamped Beam Using Homotopy Perturbation Method

2009 ◽  
Author(s):  
Mahdi Mojahedi ◽  
Hamid Moeenfard ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Axial Loading ◽  
Design Parameters ◽  
Electric Force ◽  
Homotopy Perturbation ◽  
Static Responses ◽  
Fringing Field ◽  
Fringing Field Effect ◽  
Good Agreement

In this study, static deflection and Instability of double-clamped nanobeams actuated by electrostatic field and intermolecular force, are investigated. The model accounts for the electric force nonlinearity of the excitation and for the fringing field effect. Effects of mid-plane stretching and axial loading are considered. Galerkin’s decomposition method is utilized to convert the nonlinear differential equation of motion to a nonlinear algebraic equation which is solved using the homotopy perturbation method. The effect of the design parameters such as axial load and mid-plane stretching on the static responses and pull-in instability is discussed. Results are in good agreement with presented in the literature.

scholarly journals A Simple Modification of Homotopy Perturbation Method for the Solution of Blasius Equation in Semi-Infinite Domains

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
M. Aghakhani ◽  
M. Suhatril ◽  
M. Mohammadhassani ◽  
M. Daie ◽  
A. Toghroli
Keyword(s):  
Boundary Condition ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Modification ◽  
Infinite Domains ◽  
Homotopy Perturbation ◽  
Blasius Equation ◽  
Fifth Order ◽  
Adomian’S Polynomials ◽  
Good Agreement

A simple modification of the homotopy perturbation method is proposed for the solution of the Blasius equation with two different boundary conditions. Padé approximate is used to deal with the boundary condition at infinity. The results obtained from the analytical method are compared to Howarth’s numerical solution and fifth order Runge-Kutta Fehlberg method indicating a very good agreement. The proposed method is a simple and reliable modification of homotopy perturbation method, which does not require the existence of a small parameter, linearization of the equation, or computation of Adomian’s polynomials.

Comparison of solutions of linear and non-linear shallow water wave equations using homotopy perturbation method

2017 ◽  
Vol 27 (9) ◽  
pp. 2015-2029 ◽  
Author(s):  
Perumandla Karunakar ◽  
Snehashish Chakraverty
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Homotopy Perturbation Method ◽  
Content Type ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Shallow Water Wave ◽  
Shallow Water Wave Equations ◽  
Non Linear

Purpose This paper aims to solve linear and non-linear shallow water wave equations using homotopy perturbation method (HPM). HPM is a straightforward method to handle linear and non-linear differential equations. As such here, one-dimensional shallow water wave equations have been considered to solve those by HPM. Interesting results are reported when the solutions of linear and non-linear equations are compared. Design/methodology/approach HPM was used in this study. Findings Solution of one-dimensional linear and non-linear shallow water wave equations and comparison of linear and non-linear coupled shallow water waves from the results obtained using present method. Originality/value Coupled non-linear shallow water wave equations are solved.

Solution of interval shallow water wave equations using homotopy perturbation method

2018 ◽  
Vol 35 (4) ◽  
pp. 1610-1624 ◽  
Author(s):  
Perumandla Karunakar ◽  
Snehashish Chakraverty
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Interval Uncertainty ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Shallow Water Wave ◽  
Shallow Water Wave Equations

Purpose This paper aims to present solutions of uncertain linear and non-linear shallow water wave equations. The uncertainty has been taken as interval and one-dimensional interval shallow water wave equations have been solved by homotopy perturbation method (HPM). In this study, basin depth and initial conditions have been taken as interval and the single parametric concept has been used to handle the interval uncertainty. Design/methodology/approach HPM has been used to solve interval shallow water wave equation with the help of single parametric concept. Findings Previously, few authors found solution of shallow water wave equations with crisp basin depth and initial conditions. But, in actual sense, the basin depth, as well as initial conditions, may not be found in crisp form. As such, here these are considered as uncertain in term of intervals. Hence, interval linear and non-linear shallow water wave equations are solved in this study using single parametric concept-based HPM. Originality/value As mentioned above, uncertainty is must in the above-titled problems due to the various parametrics involved in the governing differential equations. These uncertain parametric values may be considered as interval. To the best of the authors’ knowledge, no work has been reported on the solution of uncertain shallow water wave equations. But when the interval uncertainty is involved in the above differential equation, then direct methods are not available. Accordingly, single parametric concept-based HPM has been applied in this study to handle the said problems.

scholarly journals Application of Local Fractional Homotopy Perturbation Method in Physical Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Nabard Habibi ◽  
Zohre Nouri
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Models ◽  
Applied Mathematics ◽  
Nonlinear Phenomena ◽  
Homotopy Perturbation ◽  
Physical Problems ◽  
Fourier Series Method ◽  
Physical Phenomena ◽  
Good Agreement

Nonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. The perturbation method is a wave equation solution using HPM compared with the Fourier series method, and both methods results are good agreement. The percentage of error of ux,t with α=1 and 0.33, t =0.1 sec, between the present research and Yong-Ju Yang study for x≥0.6 is less than 10. Also, the % error for x≥0.5 in α=1 and 0.33, t =0.3 sec, is less than 5, whereas for α=1 and 0.33, t =0.8 and 0.7 sec, the % error for x≥0.4 is less than 8.

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