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Статті в журналах з теми "Homotopy perturbation"

Автор: Grafiati

Опубліковано: 3 червня 2025

Оновлено: 31 липня 2025

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1

Side, Syafruddin, Maya Sari Wahyuni, and Muh Rifki. "Solusi Numerik Model SIR pada Penyebaran Penyakit Hepatitis B dengan Metode Perturbasi Homotopi di Provinsi Sulawesi Selatan." Journal of Mathematics, Computations, and Statistics 3, no. 2 (2020): 79. http://dx.doi.org/10.35580/jmathcos.v3i2.20122.

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Анотація:

Penelitian ini membahas mengenai solusi secara numerik dari model SIR pada penyebaran penyakit Hepatitis B dengan Metode Perturbasi Homotopi. Data yang digunakan adalah data sekunder dari penelitian Rosdiana (2015) yang berupa model SIR dan jumlah penderita Hepatitis B di Provinsi Sulawesi Selatan tahun 2015 dari Dinas Kesehatan Provinsi Sulawesi Selatan. Pembahasan dimulai dari penentuan solusi umum dengan Metode Perturbasi Homotopi, penentuan parameter, simulasi dan analisis hasil. Setelah dilakukan analisis dari simulasi numerik terlihat bahwa Metode Perturbasi Homotopi dapat digunakan untu

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2

He, Xi Qin, and Hai Yang Li. "Based on the Improved Homotopy Perturbation Method for Solving Nonlinear Equations." Applied Mechanics and Materials 275-277 (January 2013): 836–40. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.836.

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Анотація:

According to Nonlinear Fredholm differential and integral equation，it is proposed that the improved homotopy perturbation method is used to solve in this paper, and apply the numerical examples to compare the advantages among homotopy perturbation method, Adomian decomposition method and improved homotopy perturbation method . The results show that improved homotopy perturbation method is more effective.

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3

He, Ji-Huan. "Homotopy perturbation technique." Computer Methods in Applied Mechanics and Engineering 178, no. 3-4 (1999): 257–62. http://dx.doi.org/10.1016/s0045-7825(99)00018-3.

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4

Singh, Prince, and Dinkar Sharma. "Comparative study of homotopy perturbation transformation with homotopy perturbation Elzaki transform method for solving nonlinear fractional PDE." Nonlinear Engineering 9, no. 1 (2019): 60–71. http://dx.doi.org/10.1515/nleng-2018-0136.

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Анотація:

AbstractWe apply homotopy perturbation transformation method (combination of homotopy perturbation method and Laplace transformation) and homotopy perturbation Elzaki transformation method on nonlinear fractional partial differential equation (fpde) to obtain a series solution of the equation. In this case, the fractional derivative is described in Caputo sense. To avow the adequacy and authenticity of the technique, we have applied both the techniques to Fractional Fisher’s equation, time-fractional Fornberg-Whitham equation and time fractional Inviscid Burgers’ equation. Finally, we compare

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5

Bota, Constantin, and Bogdan Căruntu. "Approximate Analytical Solutions of the Regularized Long Wave Equation Using the Optimal Homotopy Perturbation Method." Scientific World Journal 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/721865.

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Анотація:

The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results.

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6

Ihsan, Hisyam, Ahmad Zaki, and Nur Syuaiba. "Solusi Numerik Model Matematika SIRI Metode Perturbasi Homotopi dalam Penggunaan E-money Sistem E-parking." Journal of Mathematics Computations and Statistics 5, no. 1 (2022): 20. http://dx.doi.org/10.35580/jmathcos.v5i1.32246.

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Анотація:

Penelitian ini merupakan penelitian terapan mengenai penerapan metode Perturbasi Homotopi untuk mencari solusi numerik model matematika SIRI dalam penggunaan E-money sistem E-parking dengan metode Perturbasi Homotopi. Data yang digunakan adalah data yang diperoleh dengan membagikn angket kepada 236 responden secara acak di lokasi penelitian yaitu Mall Panakkukang, Mall Nipah dan Mall Ratu Indah. Pembahasan dimulai dari penentuan solusi umum dengan metode Perturbasi Homotopi, penentuan parameter, simulasi dan analisis hasil. Dalam penelitian ini diperoleh grafik pergerakan dari model SIRI denga

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7

Saeed, Rostam K., and Rebwar S. Muhammad. "Solving Coupled Hirota System by Using Homotopy Perturbation and Homotopy Analysis Methods." Journal of Zankoy Sulaimani - Part A 17, no. 2 (2015): 201–18. http://dx.doi.org/10.17656/jzs.10394.

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8

K, Nandhini, and Sumathi M. "New and Modified Homotopy Perturbation Methods for Addressing Burger's Non-linear Equation." Indian Journal of Science and Technology 17, no. 38 (2024): 4019–29. https://doi.org/10.17485/IJST/v17i38.2029.

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Анотація:

Abstract <strong>Objectives:</strong> The aim of this study is to find a novel solution procedure for solving a fluid dynamical problem, especially to solve two-dimensional coupled Burger’s non-linear equation. <strong>Methods:</strong> New and Modified homotopy perturbation techniques are used to solve the two-dimensional coupled Burger’s equation. The methods intend to make homotopy perturbation method a more robust and trustworthy tool for fluid dynamics researchers by addressing convergence concerns, improving solution accuracy and allowing it to handle a broader

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9

K.C. Mishra, K. C. Mishra. "Inverse Homotopy Perturbation Method for Nonlinear systems." International Journal of Scientific Research 2, no. 4 (2012): 61–64. http://dx.doi.org/10.15373/22778179/apr2013/86.

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10

Nandhini, K., and M. Sumathi. "New and Modified Homotopy Perturbation Methods for Addressing Burger’s Non-linear Equation." Indian Journal Of Science And Technology 17, no. 38 (2024): 4019–29. http://dx.doi.org/10.17485/ijst/v17i38.2029.

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Анотація:

Objectives: The aim of this study is to find a novel solution procedure for solving a fluid dynamical problem, especially to solve two-dimensional coupled Burger’s non-linear equation. Methods: New and Modified homotopy perturbation techniques are used to solve the two-dimensional coupled Burger’s equation. The methods intend to make homotopy perturbation method a more robust and trustworthy tool for fluid dynamics researchers by addressing convergence concerns, improving solution accuracy and allowing it to handle a broader range of problems. Findings: The solution for two-dimensional coupled

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11

Elbadri, Mohamed. "Comparison between the Homotopy Perturbation Method and Homotopy Perturbation Transform Method." Applied Mathematics 09, no. 02 (2018): 130–37. http://dx.doi.org/10.4236/am.2018.92009.

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12

S. Sekar and A. Sakthivel. "Numerical investigation of the hybrid fuzzy differential equations using He's homotopy perturbation method." Malaya Journal of Matematik 5, no. 02 (2017): 475–82. http://dx.doi.org/10.26637/mjm502/026.

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Анотація:

This paper presents an efficient method namely He's Homotopy Perturbation Method (HHPM) is introduced for solving hybrid fuzzy differential equations based on Seikkala derivative with initial value problem [2]. The proposed method is tested on hybrid fuzzy differential equations. The discrete solutions obtained through He's Homotopy Perturbation Method are compared with Leapfrog method [13]. The applicability of the He's Homotopy Perturbation Method is more suitable to solve the hybrid fuzzy differential equations. Error graphs are presented to highlight the efficiency of the He's Homotopy Per

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13

Dhumal, Meenakshi, and Bhausaheb Sontakke. "Solving Time-Fractional Fitzhugh–Nagumo Equation using Homotopy Perturbation Method." Indian Journal Of Science And Technology 17, no. 13 (2024): 1272–82. http://dx.doi.org/10.17485/ijst/v17i13.3009.

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Анотація:

Objectives: This study aims to explore solutions to the time-fractional Fitzhugh-Nagumo equation, a nonlinear reaction-diffusion equation. Method: We utilize the Homotopy Perturbation Method (HPM) as a proficient analytical approach for addressing the time-fractional Fitzhugh-Nagumo equation. The HPM offers a structured method for deriving approximate solutions in the shape of convergent series, enabling accurate solutions even for intricate nonlinear fractional equations. Finding: The series solution obtained is validated by comparing it with numerical methods, showcasing its precision and ef

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14

F. Kadhem, Mohanad, and Ali H. Alfayadh. "Mixed Homotopy Integral Transform Method for Solving Non-Linear ntegro-Differential Equation." Al-Nahrain Journal of Science 25, no. 1 (2022): 35–40. http://dx.doi.org/10.22401/anjs.25.1.06.

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Анотація:

In this paper, we have applied Sawi transform with homotopyperturbation method to obtain analytic approximation for non-linear integro-differential Equations. The proposed technique is compared with homotopy perturbation method and Abood transform homotopy perturbation method. The results show that Sawi transform homotopy perturbation is an efficient approach to solve non-linear integro-differential equations.

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15

Zayed, Elsayed M. E., Taher A. Nofal, and Khaled A. Gepreel. "The Homotopy Perturbation Method for Solving Nonlinear Burgers and New Coupled Modified Korteweg-de Vries Equations." Zeitschrift für Naturforschung A 63, no. 10-11 (2008): 627–33. http://dx.doi.org/10.1515/zna-2008-10-1103.

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Анотація:

We use the homotopy perturbation method to find the travelling wave solutions of nonlinear Burgers and new coupled modified Korteweg-de Vries equations. The results reveal that the homotopy perturbation method is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the homotopy perturbation method can find wide application in engineering and physics.

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16

Malo, Diyar Hashim, Rogash Younis Masiha, Muhammad Amin Sadiq Murad, and Sadeq Taha Abdulazeez. "A New Computational Method Based on Integral Transform for Solving Linear and Nonlinear Fractional Systems." Jurnal Matematika MANTIK 7, no. 1 (2021): 9–19. http://dx.doi.org/10.15642/mantik.2021.7.1.9-19.

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Анотація:

In this article, the Elzaki homotopy perturbation method is applied to solve fractional stiff systems. The Elzaki homotopy perturbation method (EHPM) is a combination of a modified Laplace integral transform called the Elzaki transform and the homotopy perturbation method. The proposed method is applied for some examples of linear and nonlinear fractional stiff systems. The results obtained by the current method were compared with the results obtained by the kernel Hilbert space KHSM method. The obtained result reveals that the Elzaki homotopy perturbation method is an effective and accurate t

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17

Khidir, Ahmed A. "A New Spectral-Homotopy Perturbation Method and Its Application to Jeffery-Hamel Nanofluid Flow with High Magnetic Field." Journal of Computational Methods in Physics 2013 (December 30, 2013): 1–10. http://dx.doi.org/10.1155/2013/939143.

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Анотація:

We present a new modification of the homotopy perturbation method (HPM) for solving nonlinear boundary value problems. The technique is based on the standard homotopy perturbation method, and blending of the Chebyshev pseudospectral methods. The implementation of the new approach is demonstrated by solving the Jeffery-Hamel flow considering the effects of magnetic field and nanoparticle. Comparisons are made between the proposed technique, the standard homotopy perturbation method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of the present approach

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18

Divya Bharathi S, Gerly TG, Sangeetha M, Azeeza SM, and Gomathi G. "Solving linear heat equation and wave equation using homotopy perturbation laplace-carson transform method." Journal of Computational Mathematica 8, no. 1 (2024): 094–104. http://dx.doi.org/10.26524/cm190.

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Анотація:

In this paper, we will study about the advanced method is an appropriate union of the new integral transform named as “Laplace-Carson transform" and the homotopy perturbation method. Also finding the analytical solution of the heat equation and wave equation using the homotopy perturbation Laplace-Carson transform method (HPLCTM) is merged form of Laplace-Carson transform,homotopy perturbation method and He’s polynomial.

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19

Vázquez-Leal, Héctor. "Rational Homotopy Perturbation Method." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/490342.

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Анотація:

The solution methods of nonlinear differential equations are very important because most of the physical phenomena are modelled by using such kind of equations. Therefore, this work presents a rational version of homotopy perturbation method (RHPM) as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We present two case studies; for the first example, a comparison between the proposed method and the HPM method is presented; it will show how the RHPM generates highly accurate approximate solutions requiring less iteration, in comparison to resu

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20

Alqhtani, Manal, Khaled M. Saad, Rasool Shah, Thongchai Botmar, and Waleed M. Hamanah. "Evaluation of fractional-order equal width equations with the exponential-decay kernel." AIMS Mathematics 7, no. 9 (2022): 17236–51. http://dx.doi.org/10.3934/math.2022949.

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Анотація:

<abstract><p>In this article we consider the homotopy perturbation transform method to investigate the fractional-order equal-width equations. The homotopy perturbation transform method is a mixture of the homotopy perturbation method and the Yang transform. The fractional-order derivative are defined in the sense of Caputo-Fabrizio operator. Several fractions of solutions are calculated which define some valuable evolution of the given problems. The homotopy perturbation transform method results are compared with actual results and good agreement is found. The suggested method can

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21

Singh, Jagdev, and Devendra Kumar. "Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics Equation." Journal of Applied Mathematics, Statistics and Informatics 8, no. 1 (2012): 55–61. http://dx.doi.org/10.2478/v10294-012-0006-2.

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Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics EquationIn this paper, we apply a combined form of the Laplace transform method with the homotopy perturbation method to obtain the solution of nonlinear gas dynamics equation. This method is called the homotopy perturbation transform method (HPTM). This technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that this scheme solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the de

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22

He, Ji-Huan. "Homotopy Perturbation Method with an Auxiliary Term." Abstract and Applied Analysis 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/857612.

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Анотація:

The two most important steps in application of the homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. The homotopy equation should be such constructed that when the homotopy parameter is zero, it can approximately describe the solution property, and the initial solution can be chosen with an unknown parameter, which is determined after one or two iterations. This paper suggests an alternative approach to construction of the homotopy equation with an auxiliary term; Dufing equation is used as an example to illustrate the solution p

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23

Khan, Muhammad Asim, Shafiq Ullah, and Norhashidah Hj Mohd Ali. "Application of Optimal Homotopy Asymptotic Method to Some Well-Known Linear and Nonlinear Two-Point Boundary Value Problems." International Journal of Differential Equations 2018 (December 3, 2018): 1–11. http://dx.doi.org/10.1155/2018/8725014.

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Анотація:

The objective of this paper is to obtain an approximate solution for some well-known linear and nonlinear two-point boundary value problems. For this purpose, a semianalytical method known as optimal homotopy asymptotic method (OHAM) is used. Moreover, optimal homotopy asymptotic method does not involve any discretization, linearization, or small perturbations and that is why it reduces the computations a lot. OHAM results show the effectiveness and reliability of OHAM for application to two-point boundary value problems. The obtained results are compared to the exact solutions and homotopy pe

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24

Yavuz, Mehmet, and Necati Ozdemir. "Numerical inverse Laplace homotopy technique for fractional heat equations." Thermal Science 22, Suppl. 1 (2018): 185–94. http://dx.doi.org/10.2298/tsci170804285y.

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Анотація:

In this paper, we have aimed the numerical inverse Laplace homotopy technique for solving some interesting 1-D time-fractional heat equations. This method is based on the Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method. Firstly, we have applied to the fractional 1-D PDE by using He?s polynomials. Then we have used Laplace transform method and discussed how to solve these PDE by using Laplace homotopy perturbation method. We have declared that the proposed model is very efficient and powerful technique in finding approxi

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25

Novin, Reza, and Mohammad Ali Fariborzi Araghi. "Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control." Journal of Low Frequency Noise, Vibration and Active Control 38, no. 2 (2019): 706–27. http://dx.doi.org/10.1177/1461348419827378.

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Анотація:

This paper attempts to propose and investigate a modification of the homotopy perturbation method to study hypersingular integral equations of the first kind. Along with considering this matter, of course, the novel method has been compared with the standard homotopy perturbation method. This method can be conveniently fast to get the exact solutions. The validity and reliability of the proposed scheme are discussed. Different examples are included to prove so. According to the results, we further state that new simple homotopy perturbation method is so efficient and promises the exact solutio

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26

Khidir, Ahmed A. "Spectral-Homotopy Perturbation Method for Solving Governing MHD Jeffery-Hamel Problem." Journal of Computational Methods in Physics 2014 (July 14, 2014): 1–7. http://dx.doi.org/10.1155/2014/512702.

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Анотація:

We present a new modification of the homotopy perturbation method (HPM) for solving nonlinear boundary value problems. The technique is based on the standard homotopy perturbation method and blending of the Chebyshev pseudospectral methods. The implementation of the new approach is demonstrated by solving the MHD Jeffery-Hamel flow and the effect of MHD on the flow has been discussed. Comparisons are made between the proposed technique, the previous studies, the standard homotopy perturbation method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of t

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27

Hussain, Khawlah. "New reliable modifications of HPM and HAM." Indonesian Journal of Electrical Engineering and Computer Science 19, no. 1 (2020): 371. http://dx.doi.org/10.11591/ijeecs.v19.i1.pp371-379.

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Анотація:

<p>In this article, a new modification of the homotopy perturbation method (HPM) and homotopy analysis method (HAM) is presented and applied to non-homogeneous fractional Volterra integro-differential equations with boundary conditions. A comparative study between the new modified homotopy perturbation method (MHPM) and the new modified homotopy analysis method (MHAM). Several illustrative examples are given to demonstrate the effectiveness and reliability of the methods.</p>

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28

Dhumal, Meenakshi, Bhausaheb Sontakke, and Jagdish Sonawane. "Solving Time-Space Fractional Boussinesq Equation Using Homotopy Perturbation Method." European Journal of Mathematics and Statistics 5, no. 6 (2024): 1–6. http://dx.doi.org/10.24018/ejmath.2024.5.6.377.

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Анотація:

This paper aims to implement the homotopy perturbation technique to solve the time-space fractional Boussinesq equation, a significant model in the analysis of nonlinear wave propagation. Through the application of the homotopy perturbation technique, we derive analytical expressions for the solutions of the time-space fractional Boussinesq equation and validate these solutions through comparisons with numerical methods. Obtained results demonstrate the efficiency and accuracy of the homotopy perturbation method in solving the time-space fractional Boussinesq equation.

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29

Yasmin, Humaira. "Application of Aboodh Homotopy Perturbation Transform Method for Fractional-Order Convection–Reaction–Diffusion Equation within Caputo and Atangana–Baleanu Operators." Symmetry 15, no. 2 (2023): 453. http://dx.doi.org/10.3390/sym15020453.

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Анотація:

This article is an analysis of fractional nonlinear convection–reaction–diffusion equations involving the fractional Atangana–Baleanu and Caputo derivatives. An efficient Aboodh homotopy perturbation transform method, which combines the homotopy perturbation method with the Aboodh transformation, is applied to investigate this fractional-order proposed model, analytically. A modified technique known as the Aboodh homotopy perturbation transform method is formulated to approximate these derivatives. The analytical simulation is investigated graphically as well as in tabular form.

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30

Hendi, F. A., and M. M. Al-Qarni. "An Accelerated Homotopy Perturbation Method for Solving Nonlinear Two-Dimensional Volterra-Fredholm Integrodifferential Equations." Advances in Mathematical Physics 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/9385040.

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Анотація:

We propose and apply coupling of the variational iteration method (VIM) and homotopy perturbation method (HPM) to solve nonlinear mixed Volterra-Fredholm integrodifferential equations (VFIDE). In this approach, we use a new formula called variational homotopy perturbation method (VHPM) and variational accelerated homotopy perturbation method (VAHPM). This approach is based on the form of He’s polynomials and on a new form of He’s polynomials. We discuss the convergence of the technique. Some numerical examples are introduced to verify the efficiency of this technique.

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31

Rhofir, K., A. Radid, and M. Laaraj. "SOR Homotopy perturbation method to solve integro-differential equations." Mathematical Modeling and Computing 11, no. 4 (2024): 954–65. http://dx.doi.org/10.23939/mmc2024.04.954.

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Анотація:

We present in this paper, SOR Homotopy perturbation method, a new decomposition method by introducing a parameter ω to extend a classical homotopy perturbation method for solving integro-differential equations of various kinds. Using SOR homotopy perturbation method and its iterative scheme we can give the exact solution or a closed approximate to the solution of the problem. The convergence of the proposed method has been elaborated and some illustrative examples are presented with applications to Fredholm and Volterra integral equations.

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32

S. Sekar and A. S. Thirumurugan. "Numerical investigation of the nonlinear integro-differential equations using He's homotopy perturbation method." Malaya Journal of Matematik 5, no. 02 (2017): 389–94. http://dx.doi.org/10.26637/mjm502/016.

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Анотація:

In this paper, He's Homotopy Perturbation Method (HHPM), by construction, produces approximate solutions of nonlinear integro-differential equations [2]. The purpose of this paper is to extend the He's Homotopy Perturbation method to the nonlinear integro-differential equations. Efficient error estimation for the He's Homotopy Perturbation method is also introduced. Details of this method are presented and compared with Single-Term Haar Wavelet Series (STHWS) method [2] numerical results along with estimated errors are given to clarify the method and its error estimator.

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33

Fatima, Nahid, Kamal Shah, and Thabet Abdeljawad. "Porous medium equation with Elzaki transform homotopy perturbation." Thermal Science 27, Spec. issue 1 (2023): 1–8. http://dx.doi.org/10.2298/tsci23s1001f.

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Анотація:

We have shown how to solve 1-D fourth order parabolic linear PDE with varable coefficients in this article. We have applied the Elzaki transform homotopy pertur?bation method. It is used in conjunction with the homotopy perturbation approach in this method. To further showcase the Elzaki transform-homotopy perturbation technique?s competence and reliability, we have provided solution the parabolic linear PDE. It was found that both HPM and Laplace decomposition method were similar when compared to resulting analytical solutions. Results suggest that the Elzaki transform in conjunction with the

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34

Ali, Liaqat, Saeed Islam, Taza Gul, and Iraj Sadegh Amiri. "Solution of nonlinear problems by a new analytical technique using Daftardar-Gejji and Jafari polynomials." Advances in Mechanical Engineering 11, no. 12 (2019): 168781401989696. http://dx.doi.org/10.1177/1687814019896962.

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Анотація:

This article shows the solution of nonlinear differential equations by a new analytical technique called modified optimal homotopy perturbation method. Daftardar-Gejji and Jafari polynomials are used in the proposed method for the expansion of nonlinear term in the equation. Four nonlinear boundary value problems of fourth, fifth, sixth, and eighth orders are solved by modified optimal homotopy perturbation method as well as optimal homotopy perturbation method. The achieved consequences are authenticated by comparison with the results gained by the existing method—optimal homotopy perturbatio

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35

Saadeh, Rania, Ahmad Qazza, and Abdelilah Kamal Sedeeg. "A Generalized Hybrid Method for Handling Fractional Caputo Partial Differential Equations via Homotopy Perturbed Analysis." WSEAS TRANSACTIONS ON MATHEMATICS 22 (December 31, 2023): 988–1000. http://dx.doi.org/10.37394/23206.2023.22.108.

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Анотація:

This article describes a novel hybrid technique known as the Sawi transform homotopy perturbation method for solving Caputo fractional partial differential equations. Combining the Sawi transform and the homotopy perturbation method, this innovative technique approximates series solutions for fractional partial differential equations. The Sawi transform is a recently developed integral transform that may successfully manage recurrence relations and integro-differential equations. Using a homotopy parameter, the homotopy perturbation method is a potent semi-analytical tool for constructing appr

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36

Dubey, Ravi Shanker, Badr Saad T. Alkahtani, and Abdon Atangana. "Analytical Solution of Space-Time Fractional Fokker-Planck Equation by Homotopy Perturbation Sumudu Transform Method." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/780929.

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Анотація:

An efficient approach based on homotopy perturbation method by using Sumudu transform is proposed to solve some linear and nonlinear space-time fractional Fokker-Planck equations (FPEs) in closed form. The space and time fractional derivatives are considered in Caputo sense. The homotopy perturbation Sumudu transform method (HPSTM) is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. Some examples show that the HPSTM is an effective tool for solving many space time fractional partia

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37

Mohand, M. Abdelrahim Mahgoub*. "HOMOTOPY PERTURBATION AND ABOODH TRANSFORM FOR SOLVING SINE-GORDEN AND KLEIN-GORDEN EQUATIONS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, no. 10 (2016): 48–53. https://doi.org/10.5281/zenodo.159283.

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Анотація:

In this paper, we practiced relatively new, analytical method known as the homotopy perturbation method (HPM) and Aboodh transform is employed to obtain the approximate analytical solution of the Klein–Gordon and sine-Gordon equations. The nonlinear terms can be handled by the use of homotopy perturbation method. The proposed homotopy perturbation method is applied to reformulate the first and the second order initial value problems which leads to the solution in terms of transformed variable, and the series solution that can be obtained by making use of the inverse transformation.

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38

Kappeler, T., S. Kuksin, and V. Schroeder. "Perturbations of the Harmonic Map Equation." Communications in Contemporary Mathematics 05, no. 04 (2003): 629–69. http://dx.doi.org/10.1142/s0219199703001087.

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We consider perturbations of the harmonic map equation in the case where the target manifold is a closed Riemannian manifold of nonpositive sectional curvature. For any semilinear and, under some extra conditions, quasilinear perturbation, the space of classical solutions within a homotopy class is proved to be compact. An important ingredient for our analysis is a new inequality for maps in a given homotopy class which can be viewed as a version of the Poincaré inequality for such maps.

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39

SABERI-NADJAFI, JAFAR, and MOHAMADREZA TAMAMGAR. "MODIFIED HOMOTOPY PERTURBATION METHOD FOR SOLVING INTEGRAL EQUATIONS." International Journal of Modern Physics B 24, no. 24 (2010): 4741–46. http://dx.doi.org/10.1142/s0217979210056189.

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This paper proposes a modified homotopy perturbation method to solve Fredholm and Volterra integral equations. Comparison of the obtained results with those obtained by the standard homotopy perturbation method shows that the proposed method is very effective and simple.

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40

HE, JI-HUAN. "ADDENDUM: NEW INTERPRETATION OF HOMOTOPY PERTURBATION METHOD." International Journal of Modern Physics B 20, no. 18 (2006): 2561–68. http://dx.doi.org/10.1142/s0217979206034819.

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The present work constitutes a guided tour through the mathematics needed for a proper understanding of homotopy perturbation method as applied to various nonlinear problems. It gives a new interpretation of the concept of constant expansion in the homotopy perturbation method.

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41

Gad-Allah, Musa R., and Tarig M. Elzaki. "Application of New Homotopy Perturbation Method for Solving Partial Differential Equations." Journal of Computational and Theoretical Nanoscience 15, no. 2 (2018): 500–508. http://dx.doi.org/10.1166/jctn.2018.6725.

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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

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42

Atindiga, Terhemen Simon, Ezike Godwin Mbah, Ndidiamaka Edith Didigwu, Adebisi Raphael Adewoye, and Torkuma Bartholomew Kper. "Approximate Solution of an Infectious Disease Model Applying Homotopy Perturbation Method." Global Journal of Health Science 12, no. 5 (2020): 64. http://dx.doi.org/10.5539/gjhs.v12n5p64.

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Scientists and engineers have developed the use of Homotopy Perturbation Method (HPM) in non-linear problems since this approach constantly distort the intricate problem being considered into a simple problem, thus making it much less complex to solve. The homotopy perturbation method was initially put forward by He (1999) with further development and improvement (He 2000a, He, 2006). Homotopy, which is as an essential aspect of differential topology involves a coupling of the conventional perturbation method and the homotopy method in topology (He, 2000b). The approach gives an approximate an

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Chun, Changbum. "Application of Homotopy Perturbation Method with Chebyshev Polynomials to Nonlinear Problems." Zeitschrift für Naturforschung A 65, no. 1-2 (2010): 65–70. http://dx.doi.org/10.1515/zna-2010-1-206.

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AbstractIn this paper, we present an efficient modification of the homotopy perturbation method by using Chebyshev’s polynomials and He’s polynomials to solve some nonlinear differential equations. Some illustrative examples are given to demonstrate the efficiency and reliability of the modified homotopy perturbation method.

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Jafari, Hossein, Khadijeh Bagherian, and Seithuti P. Moshokoa. "Homotopy Perturbation Method to Obtain Positive Solutions of Nonlinear Boundary Value Problems of Fractional Order." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/919052.

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We use the homotopy perturbation method for solving the fractional nonlinear two-point boundary value problem. The obtained results by the homotopy perturbation method are then compared with the Adomian decomposition method. We solve the fractional Bratu-type problem as an illustrative example.

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45

Meenakshi, Dhumal, and Sontakke Bhausaheb. "Solving Time-Fractional Fitzhugh–Nagumo Equation using Homotopy Perturbation Method." Indian Journal of Science and Technology 17, no. 13 (2024): 1272–82. https://doi.org/10.17485/IJST/v17i13.3009.

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Abstract <strong>Objectives:</strong> This study aims to explore solutions to the time-fractional Fitzhugh-Nagumo equation, a nonlinear reaction-diffusion equation. <strong>Method:</strong> We utilize the Homotopy Perturbation Method (HPM) as a proficient analytical approach for addressing the time-fractional Fitzhugh-Nagumo equation. The HPM offers a structured method for deriving approximate solutions in the shape of convergent series, enabling accurate solutions even for intricate nonlinear fractional equations. <strong>Finding:</strong> The series solution obtained

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Devi, A., and M. Jakhar. "A Reliable Computational Algorithm for Solving Fractional Biological Population Model." Journal of Scientific Research 13, no. 1 (2021): 59–71. http://dx.doi.org/10.3329/jsr.v13i1.47521.

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Анотація:

In this work, authors obtained the series solution of nonlinear fractional partial differential equations, which is emerging in a spatial diffusion of biological population model using Elzaki transform homotopy perturbation method (ETHPM). The Elzaki transform homotopy perturbation method is a combined form of the Elzaki transform and homotopy perturbation method. Three test illustrations are used to show the proficiency and accuracy of the projected method. It has been observed that the proposed technique can be widely employed to examine other real world problems. The results obtained with t

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47

Devi, A., and M. Jakhar. "A Reliable Computational Algorithm for Solving Fractional Biological Population Model." Journal of Scientific Research 13, no. 1 (2021): 59–71. http://dx.doi.org/10.3329/jsr.v13i1.47521.

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Анотація:

In this work, authors obtained the series solution of nonlinear fractional partial differential equations, which is emerging in a spatial diffusion of biological population model using Elzaki transform homotopy perturbation method (ETHPM). The Elzaki transform homotopy perturbation method is a combined form of the Elzaki transform and homotopy perturbation method. Three test illustrations are used to show the proficiency and accuracy of the projected method. It has been observed that the proposed technique can be widely employed to examine other real world problems. The results obtained with t

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48

He, J. H. "Asymptotology by homotopy perturbation method." Applied Mathematics and Computation 156, no. 3 (2004): 591–96. http://dx.doi.org/10.1016/j.amc.2003.08.011.

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He, Ji-Huan. "Comparison of homotopy perturbation method and homotopy analysis method." Applied Mathematics and Computation 156, no. 2 (2004): 527–39. http://dx.doi.org/10.1016/j.amc.2003.08.008.

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50

Cuce, Erdem, and Pinar Mert Cuce. "Homotopy perturbation method for temperature distribution, fin efficiency and fin effectiveness of convective straight fins with temperature-dependent thermal conductivity." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 8 (2012): 1754–60. http://dx.doi.org/10.1177/0954406212469579.

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Анотація:

Homotopy perturbation method is a novel approach that provides an approximate analytical solution to differential equations in the form of an infinite power series. In our previous work, homotopy perturbation method has been used to evaluate thermal performance of straight fins with constant thermal conductivity. A dimensionless analytical expression has been developed for fin effectiveness. In this study, homotopy perturbation method has been applied to convective straight fins considering thermal conductivity of the fin material is a function of the fin temperature. Former expression for fin

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