Homotopy perturbation method for homogeneous Smoluchowsk's equation

Biazar, Jafar; Ayati, Zainab; Yaghouti, Mohammad Reza

doi:10.1002/num.20480

Cited by 17 publications

(10 citation statements)

References 14 publications

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“…This equation is widely applied to describe the time evolution of the cluster-size distribution during aggregation processes. In this paper, the following Smoluchowski's equation [5,6], will be considered; ( , ) ( ) ( ), , ,…”

Section: Homogeneous Smoluchowski Coagulation Equationmentioning

confidence: 99%

New Method for Homogeneous Smoluchowski Coagulation Equation

H¹

2015

J Appl Computat Math

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Section: Homogeneous Smoluchowski Coagulation Equationmentioning

confidence: 99%

New Method for Homogeneous Smoluchowski Coagulation Equation

H¹

2015

J Appl Computat Math

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“…Homotopy perturbation method was used to find the exact or the approximate solutions of the linear and nonlinear integral equations [16,18], the two-dimensional integral equations [19][20][21], and the integrodifferential equations [22][23][24][25]. This method enables seeking a solution of the following operator equation:…”

Section: The Solution Of Two-phase Inverse Stefan Problemmentioning

confidence: 99%

“…In this section, the homotopy perturbation method is applied to solve the inverse problem. We make the homotopy map for (22):…”

Section: The Solution Of the Two-phase Inverse Stefan Problemmentioning

confidence: 99%

The Solution of Two-Phase Inverse Stefan Problem Based on a Hybrid Method with Optimization

Luo

Cui

2015

Mathematical Problems in Engineering

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The two-phase Stefan problem is widely used in industrial field. This paper focuses on solving the two-phase inverse Stefan problem when the interface moving is unknown, which is more realistic from the practical point of view. With the help of optimization method, the paper presents a hybrid method which combines the homotopy perturbation method with the improved Adomian decomposition method to solve this problem. Simulation experiment demonstrates the validity of this method. Optimization method plays a very important role in this paper, so we propose a modified spectral DY conjugate gradient method. And the convergence of this method is given. Simulation experiment illustrates the effectiveness of this modified spectral DY conjugate gradient method.

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“…Later, He (1999b, 2003, 2020b) introduced another method called homotopy perturbation method (HPM) to solve PDEs which convert the results into the form of a series. Many authors (Biazar et al , 2010; Biazar and Ghazvini, 2009; Taşcan and Özer, 2010) applied this technique and showed that HPM is an excellent technique which converges to the exact solution very rapidly. Khan and Wu (2011) showed that HPM is an efficient tool for nonlinear equations using He’s polynomials.…”

Section: Introductionmentioning

confidence: 99%

Analytical approach for the temperature distribution in the casting-mould heterogeneous system

Nadeem

Habib

et al. 2021

HFF

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Purpose The main purpose of this paper is to calculate the analytical solution or a closed-form solution for the temperature distribution in the heterogeneous casting-mould system. Design/methodology/approach First, the authors formulate and analyze the mathematical formulation of heat conduction equation in the heterogeneous casting-mould system, with an arbitrary assumption of the ideal contact at the cast-mould contact point. Then, He-Laplace method, based on variational iteration method (VIM), Laplace transform and homotopy perturbation method (HPM), is used to elaborate the analytical solution of this system. The main focus of He-Laplace method is to find the Lagrange multiplier with an easy approach which enables the implementation of HPM very smoothly and provides the series solution very close to the exact solution. Findings An example is considered to show that He-Laplace method provides the efficient results for calculating the temperature distribution in the casting-mould heterogeneous system. Graphical representation and error distribution represents that He-Laplace method is very simple to implement and effective for casting-mould heterogeneous system. Originality/value The work in this paper is original and advanced. Specially, calculation of Lagrange multiplier for casting-mould system has not been reported in the literature for this work.

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Homotopy perturbation method for homogeneous Smoluchowsk's equation

Cited by 17 publications

References 14 publications

New Method for Homogeneous Smoluchowski Coagulation Equation

New Method for Homogeneous Smoluchowski Coagulation Equation

The Solution of Two-Phase Inverse Stefan Problem Based on a Hybrid Method with Optimization

Analytical approach for the temperature distribution in the casting-mould heterogeneous system

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