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Relevant bibliographies by topics / Homotopy perturbation method

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Academic literature on the topic 'Homotopy perturbation method'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Homotopy perturbation method"

1

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Homotopy perturbation method"

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Thapa, Chandra B. "On the Homotopy Perturbation Method for Nonlinear Oscillators." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1570793395580841.

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Sahoo, Malika. "Some Applications of Homotopy Perturbation Method." Thesis, 2015. http://ethesis.nitrkl.ac.in/7072/1/Some_Sahoo_2015.pdf.

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In this thesis paper, I review the basic idea of Homotopy perturbation method (HPM), Modified Homotopy perturbation method (MHPM) and Homotopy perturbation transform method (HPTM). Then apply these on some higher order non-linear problems.Further, I tried to compare the results obtained from Modified homotopy perturbation method with HPM using the Sine-Gordon and fractional Klein-Gordon equation respectively. Homotopy perturbation transform method is the coupling of homotopy perturbation and Laplace transform method. Lastly, I applied the homotopy perturbation and homotopy perturbation transfo

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Liu, Kai-yuan, and 劉凱元. "Homotopy Perturbation Method for Van Der Pol Equation." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/63672681267689054510.

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碩士<br>國立政治大學<br>應用數學研究所<br>93<br>In this thesis, we study the limit cycle of van der Pol equation for parameter ε>0. We give some approximate results to the limit cycle by using the modified homotopy perturbation technique. In constract to the traditional perturbation methods, this homotopy method does not require a small parameter in the equation. Besides, we also devise a new algorithm to find the approximate amplitude and frequency of the limit cycle.

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Oguntala, George A., G. Sobamowo, Y. Ahmed, and Raed A. Abd-Alhameed. "Application of approximate analytical technique using the homotopy perturbation method to study the inclination effect on the thermal behavior of porous fin heat sink." 2018. http://hdl.handle.net/10454/16637.

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Yes<br>This article presents the homotopy perturbation method (HPM) employed to investigate the effects of inclination on the thermal behavior of a porous fin heat sink. The study aims to review the thermal characterization of heat sink with the inclined porous fin of rectangular geometry. The study establishes that heat sink of an inclined porous fin shows a higher thermal performance compared to a heat sink of equal dimension with a vertical porous fin. In addition, the study also shows that the performance of inclined or tilted fin increases with decrease in length–thickness aspect rat

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Ncube, Mahluli Naisbitt. "The natural transform decomposition method for solving fractional differential equations." Diss., 2018. http://hdl.handle.net/10500/25348.

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In this dissertation, we use the Natural transform decomposition method to obtain approximate analytical solution of fractional differential equations. This technique is a combination of decomposition methods and natural transform method. We use the Adomian decomposition, the homotopy perturbation and the Daftardar-Jafari methods as our decomposition methods. The fractional derivatives are considered in the Caputo and Caputo- Fabrizio sense.<br>Mathematical Sciences<br>M. Sc. (Applied Mathematics)

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Books on the topic "Homotopy perturbation method"

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Liao, Shijun. Beyond perturbation: Introduction to homotopy analysis method. Chapman & Hall/CRC Press, 2004.

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Beyond perturbation: Introduction to the homotopy analysis method. Chapman & Hall/CRC Press, 2004.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method (Modern Mathematics and Mechanics). Chapman & Hall/CRC, 2003.

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Soori, Mohsen, and S. Salman Nourazar. On the Exact Solution of Nonlinear Differential Equations Using Variational Iteration Method and Homotopy Perturbation Method. GRIN Verlag GmbH, 2019.

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Motives, quantum field theory, and pseudodifferential operators: Conference on Motives, Quantum Field Theory, and Pseudodifferential Operators, June 2-13, 2008, Boston University, Boston, Massachusetts. American Mathematical Society, 2010.

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Book chapters on the topic "Homotopy perturbation method"

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Marinca, Vasile, and Nicolae Herisanu. "The Optimal Homotopy Perturbation Method." In Nonlinear Dynamical Systems in Engineering. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22735-6_7.

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Odibat, Zaid, and Cyrille Bertelle. "Application of Homotopy Perturbation Method for Ecosystems Modelling." In Understanding Complex Systems. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-88073-8_5.

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Zephania, C. F. Sagar, and Tapas Sil. "An improved homotopy perturbation method to study damped oscillators." In Aerospace and Associated Technology. Routledge, 2022. http://dx.doi.org/10.1201/9781003324539-70.

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Zulkarnain, F. S., Z. K. Eshkuvatov, N. M. A. Nik Long, and F. Ismail. "Modified Homotopy Perturbation Method for Fredholm–Volterra Integro-Differential Equation." In Recent Advances in Mathematical Sciences. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-0519-0_4.

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Dubey, Shweta, and S. Chakraverty. "Homotopy Perturbation Method for Solving Fuzzy Fractional Heat-Conduction Equation." In Advances in Fuzzy Integral and Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73711-5_6.

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Jani, Haresh P., and Twinkle R. Singh. "Aboodh Transform Homotopy Perturbation Method for Solving Newell–Whitehead–Segel Equation." In Computational and Analytic Methods in Biological Sciences. River Publishers, 2023. http://dx.doi.org/10.1201/9781003393238-9.

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Yazid, Nazatulsyima Mohd, Kim Gaik Tay, Yaan Yee Choy, and Azila Md Sudin. "Solving Nonlinear Schrodinger Equation with Variable Coefficient Using Homotopy Perturbation Method." In Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015). Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2772-7_26.

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Fatima, Nahid, and Monika Dhariwal. "Solutions of Differential Equations for Prediction of COVID-19 Cases by Homotopy Perturbation Method." In Intelligent Computing Applications for COVID-19. CRC Press, 2021. http://dx.doi.org/10.1201/9781003141105-3.

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Georgieva, Atanaska, and Artan Alidema. "Convergence of Homotopy Perturbation Method for Solving of Two-Dimensional Fuzzy Volterra Functional Integral Equations." In Advanced Computing in Industrial Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97277-0_11.

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Jyoti, Sumeet Gill, Rajbala Rathee, and Neha Phogat. "The Effects of Lipid Concentration on Blood Flow Through Constricted Artery Using Homotopy Perturbation Method." In Emerging Trends in Expert Applications and Security. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-1909-3_7.

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Conference papers on the topic "Homotopy perturbation method"

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Liu, Yapeng, and Xiaoshan Zhao. "Application of Homotopy Perturbation Method in Solving Fractional Cahn-Allen Equation." In 2024 3rd International Conference on Cloud Computing, Big Data Application and Software Engineering (CBASE). IEEE, 2024. https://doi.org/10.1109/cbase64041.2024.10824608.

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Biazar, Jafar, Zainab Ayati, and Hamideh Ebrahimi. "Comparing Homotopy Perturbation Method and Adomian Decomposition Method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991054.

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Gupta, Neelam, and Neel Kanth. "Study of heat flow in a rod using homotopy analysis method and homotopy perturbation method." In EMERGING TRENDS IN MATHEMATICAL SCIENCES AND ITS APPLICATIONS: Proceedings of the 3rd International Conference on Recent Advances in Mathematical Sciences and its Applications (RAMSA-2019). Author(s), 2019. http://dx.doi.org/10.1063/1.5086635.

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Chen, Xiu Rong, and Jia Shang Yu. "The Homotopy Analysis Method to Solve Perturbation MKdV Equation." In 2012 International Conference on Computer Science and Electronics Engineering (ICCSEE). IEEE, 2012. http://dx.doi.org/10.1109/iccsee.2012.422.

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Sornkaew, Pilasluck. "Laplace homotopy perturbation method for the Rosenau–Hyman equations." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON APPLIED SCIENCE AND TECHNOLOGY (ICAST’18). Author(s), 2018. http://dx.doi.org/10.1063/1.5055539.

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Dasanayake, Isuru, Anatoly Zlotnik, Wei Zhang, and Jr-Shin Li. "Optimal control of neurons using the homotopy perturbation method." In 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). IEEE, 2013. http://dx.doi.org/10.1109/cdc.2013.6760401.

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Jassim, Hassan Kamil, Ali Thamir Salman, Hijaz Ahmad, Nabeel Jawad Hassan, and Ayed E. Hashoosh. "Solving nonlinear fractional PDEs by Elzaki homotopy perturbation method." In 2ND INTERNATIONAL CONFERENCE OF MATHEMATICS, APPLIED SCIENCES, INFORMATION AND COMMUNICATION TECHNOLOGY. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0161551.

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Almousa, Mohammad, and Ahmad Izani Ismail. "Numerical solution of Fredholm-Hammerstein integral equations by using optimal homotopy asymptotic method and homotopy perturbation method." In PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): Germination of Mathematical Sciences Education and Research towards Global Sustainability. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4887570.

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Mojahedi, Mahdi, Hamid Moeenfard, and Mohammad Taghi Ahmadian. "Nonlinear Vibration and Buckling Analysis of Beams Using Homotopy Perturbation Method." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-39592.

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In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational and buckling analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin’s decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies and critical axial loads of the beams. Effects of d

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Fatima, Nahid. "Homotopy Perturbation Method for Solving Boussinesq and Fishers Type Equations." In 2016 Second International Conference on Computational Intelligence & Communication Technology (CICT). IEEE, 2016. http://dx.doi.org/10.1109/cict.2016.101.

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