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Relevant bibliographies by topics / Optimal Homotopy Asymptotic Method (OHAM)

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Academic literature on the topic 'Optimal Homotopy Asymptotic Method (OHAM)'

Author: Grafiati

Published: 7 June 2025

Last updated: 16 July 2025

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Journal articles on the topic "Optimal Homotopy Asymptotic Method (OHAM)"

1

Biazar, Jafar, and Saghi Safaei. "Applications of OHAM and MOHAM for Fractional Seventh-Order SKI Equations." Journal of Applied Mathematics 2021 (December 31, 2021): 1–8. http://dx.doi.org/10.1155/2021/6898282.

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In this article, a comparative study between optimal homotopy asymptotic method and multistage optimal homotopy asymptotic method is presented. These methods will be applied to obtain an approximate solution to the seventh-order Sawada-Kotera Ito equation. The results of optimal homotopy asymptotic method are compared with those of multistage optimal homotopy asymptotic method as well as with the exact solutions. The multistage optimal homotopy asymptotic method relies on optimal homotopy asymptotic method to obtain an analytic approximate solution. It actually applies optimal homotopy asymptotic method in each subinterval, and we show that it achieves better results than optimal homotopy asymptotic method over a large interval; this is one of the advantages of this method that can be used for long intervals and leads to more accurate results. As far as the authors are aware that multistage optimal homotopy asymptotic method has not been yet used to solve fractional partial differential equations of high order, we have shown that this method can be used to solve these problems. The convergence of the method is also addressed. The fractional derivatives are described in the Caputo sense.

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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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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 perturbation method (HPM).

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Mahmoud, Alzubi Muath Talal, Farah Aini Abdullah, Ali Fareed Jameel, and Adila Aida Azahar. "Fuzzy Volterra Integral Equation Approximate Solution Via Optimal Homotopy Asymptotic Methods." Statistics, Optimization & Information Computing 13, no. 6 (2025): 2487–510. https://doi.org/10.19139/soic-2310-5070-2302.

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The field of fuzzy integral equations (FIEs) is significant for modeling complex, time-delayed, and uncertain physical phenomena. Nevertheless, the majority of current solutions for FIEs encounter considerable challenges, such as the inability to manage intricate fuzzy functions, stringent assumptions regarding the forms of fuzzy operations utilized, and numerical instability in extremely nonlinear issues. Moreover, the capability of traditional methods in producing precise or reliable outcomes for practical applications is limited, and if they can, will incur substantial computing expenses. These challenges underscore the demand for more effective and efficient methodologies. This study aims to address the demand by developing two approximate analytical techniques to solve the FIEs namely optimal homotopy asymptotic method (OHAM) and the multistage optimal homotopy asymptotic method (MOHAM). A novel iteration of fuzzy OHAM and MOHAM is introduced by integrating the fundamental concepts of these methodologies with fuzzy set theory and optimization techniques. Then, OHAM and MOHAM are further formulated to solve the second-kind linear Volterra fuzzy integral equations (VFIEs). These methods are named fuzzy Volterra optimal homotopy asymptotic method (FV-OHAM) and fuzzy Volterra multistage optimal homotopy asymptotic method (FV-MOHAM), respectively. From two linear examples, FV-MOHAM and FV-OHAM generated significantly more accurate results than other existing methods. A thorough assessment is performed to evaluate their effectiveness and practical use, potentially aiding in solving complex problems across several scientific and engineering fields.

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Zuhra, S., S. Islam, M. Idrees, Rashid Nawaz, I. A. Shah, and H. Ullah. "Solving Singular Boundary Value Problems by Optimal Homotopy Asymptotic Method." International Journal of Differential Equations 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/287480.

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In this paper, optimal homotopy asymptotic method (OHAM) for the semianalytic solutions of nonlinear singular two-point boundary value problems has been applied to several problems. The solutions obtained by OHAM have been compared with the solutions of another method named as modified adomain decomposition (MADM). For testing the success of OHAM, both of the techniques have been analyzed against the exact solutions in all problems. It is proved by this paper that solutions of OHAM converge rapidly to the exact solution and show most effectiveness as compared to MADM.

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Ullah, Hakeem, Saeed Islam, Muhammad Idrees, Mehreen Fiza, and Zahoor Ul Haq. "An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation." International Journal of Differential Equations 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/106934.

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We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM). We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM) and homotopy perturbation method (HPM) solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

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Younas, H., Muhammad Mustahsan, Tareq Manzoor, Nadeem Salamat, and S. Iqbal. "Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method." Mathematics 7, no. 3 (2019): 264. http://dx.doi.org/10.3390/math7030264.

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In this article, Optimal Homotopy Asymptotic Method (OHAM) is used to approximate results of time-fractional order Fokker-Planck equations. In this work, 3rd order results obtained through OHAM are compared with the exact solutions. It was observed that results from OHAM have better convergence rate for time-fractional order Fokker-Planck equations. The solutions are plotted and the relative errors are tabulated.

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Biazar, Jafar, and Roya Montazeri. "Optimal Homotopy Asymptotic and Multistage Optimal Homotopy Asymptotic Methods for Solving System of Volterra Integral Equations of the Second Kind." Journal of Applied Mathematics 2019 (January 3, 2019): 1–17. http://dx.doi.org/10.1155/2019/3037273.

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In this paper, optimal homotopy asymptotic method (OHAM) and its implementation on subinterval, called multistage optimal homotopy asymptotic method (MOHAM), are presented for solving linear and nonlinear systems of Volterra integral equations of the second kind. To illustrate these approaches two examples are presented. The results confirm the efficiency and ability of these methods for such equations. The results will be compared to find out which method is more accurate. Advantages of applying MOHAM are also illustrated.

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Muhammad, Mustahsan, Muhammad Younas Hafiz, Salamat Nadeem, Touqeer Muhammad, and Abbas Muntazim. "Modeling the thermo physical behavior of metallic porous fin on varying convective loads." Indian Journal of Science and Technology 14, no. 6 (2021): 558–72. https://doi.org/10.17485/IJST/v14i6.1761.

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Abstract <strong>Background/ Objectives:</strong> Porous-permeable structured fins are the principal operational mechanism for enhancing the percentage of heat evolved and dissipated because of their many thermo physical characteristics. Study of thermal gradients on the basis of convective loads in porous fins is important in many engineering fields. <strong>Methods:</strong> In the present fractional investigation, well-established optimal homotopy asymptotic method (OHAM) has been applied on thermal system expressed in nonlinear fractional order of ordinary differential equations for Darcy’s approach for porous-structured fin. Hereparameters related to porosity, permeability and convection have been deliberated. In order to study the thermal solicitations, the thermal analysis with insulated tip of copper based alloy is studied. <strong>Findings:</strong> It is found that porosity of system is influencing more than other factors. <strong>Novelty:</strong> This study demonstrates the efficiency of OHAM as well. <strong>Keywords:</strong> Porous; thermal; Optimal Homotopy Asymptotic Method (OHAM); darcy  

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Okundalaye, Oluwaseun Olumide, and Wan Ainun Mior Othman. "A New Optimal Homotopy Asymptotic Method for Fractional Optimal Control Problems." International Journal of Differential Equations 2021 (May 15, 2021): 1–10. http://dx.doi.org/10.1155/2021/6633130.

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Solving fractional optimal control problems (FOCPs) with an approximate analytical method has been widely studied by many authors, but to guarantee the convergence of the series solution has been a challenge. We solved this by integrating the Galerkin method of optimization technique into the whole region of the governing equations for accurate optimal values of control-convergence parameters C j s . The arbitrary-order derivative is in the conformable fractional derivative sense. We use Euler–Lagrange equation form of necessary optimality conditions for FOCPs, and the arising fractional differential equations (FDEs) are solved by optimal homotopy asymptotic method (OHAM). The OHAM technique speedily provides the convergent approximate analytical solution as the arbitrary order derivative approaches 1. The convergence of the method is discussed, and its effectiveness is verified by some illustrative test examples.

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Ullah, H., S. Islam, M. Idrees, and M. Fiza. "Solution of the Differential-Difference Equations by Optimal Homotopy Asymptotic Method." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/520467.

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We applied a new analytic approximate technique, optimal homotopy asymptotic method (OHAM), for treatment of differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Volterra equation in different form. It provides us with a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier, and explicit.

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Books on the topic "Optimal Homotopy Asymptotic Method (OHAM)"

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Marinca, Vasile, and Nicolae Herisanu. The Optimal Homotopy Asymptotic Method. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15374-2.

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Marinca, Vasile, and Nicolae Herisanu. Optimal Homotopy Asymptotic Method: Engineering Applications. Springer, 2015.

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Marinca, Vasile, and Nicolae Herisanu. Optimal Homotopy Asymptotic Method: Engineering Applications. Springer, 2016.

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Marinca, Vasile, and Nicolae Herisanu. The Optimal Homotopy Asymptotic Method: Engineering Applications. Springer, 2015.

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Book chapters on the topic "Optimal Homotopy Asymptotic Method (OHAM)"

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Shah, Qayyum. "Applications of Optimal Homotopy Asymptotic Method (OHAM) to Tenth Order Boundary Value Problem." In Lecture Notes in Civil Engineering. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-4355-1_66.

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AbstractThe aim of this paper is to apply the Optimal Homotopy Asymptotic Method (OHAM), a semi-numerical and semi-analytic technique for solving linear and nonlinear Tenth order boundary value problems. The approximate solution of the problem is calculated in terms of a rapidly convergent series. Two bench mark examples have been considered to illustrate the efficiency and implementation of the method and the results are compared with the Variational Iteration Method (VIM). An interesting result of the analysis is that, the OHAM solution is more accurate than the VIM. Moreover, OHAM provides us with a convenient way to control the convergence of approximate solutions. The obtained solutions have shown that OHAM is effective, simpler, easier and explicit.

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Marinca, Vasile, and Nicolae Herisanu. "Optimal Homotopy Asymptotic Method." In The Optimal Homotopy Asymptotic Method. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15374-2_2.

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3

Marinca, Vasile, and Nicolae Herisanu. "The Optimal Homotopy Asymptotic Method." In Nonlinear Dynamical Systems in Engineering. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22735-6_6.

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Marinca, Vasile, and Nicolae Herisanu. "Introduction." In The Optimal Homotopy Asymptotic Method. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15374-2_1.

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Marinca, Vasile, and Nicolae Herisanu. "The First Alternative of the Optimal Homotopy Asymptotic Method." In The Optimal Homotopy Asymptotic Method. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15374-2_3.

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Marinca, Vasile, and Nicolae Herisanu. "The Second Alternative of the Optimal Homotopy Asymptotic Method." In The Optimal Homotopy Asymptotic Method. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15374-2_4.

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Marinca, Vasile, and Nicolae Herisanu. "The Third Alternative of the Optimal Homotopy Asymptotic Method." In The Optimal Homotopy Asymptotic Method. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15374-2_5.

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8

Shamseldeen, Samir, Ahmed Elsaid, and Seham Madkour. "On the Approximate Solution of Caputo-Riesz-Feller Fractional Diffusion Equation." In Advanced Applications of Fractional Differential Operators to Science and Technology. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-3122-8.ch010.

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In this work, a space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative is introduced. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. Also, a very useful Riesz-Feller fractional derivative is proved; the property is essential in applying iterative methods specially for complex exponential and/or real trigonometric functions. The analytic series solution of the problem is obtained via the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to highlight the effect of changing the fractional derivative parameters on the behavior of the obtained solutions. The results in this work are originally extracted from the author's work.

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Okundalaye, Oluwaseun O., Necati Özdemir, and Wan A. M. Othman. "A New Method of Multistage Optimal Homotopy Asymptotic Method for Solution of Fractional Optimal Control Problem." In Fractional Calculus: New Applications in Understanding Nonlinear Phenomena. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9789815051933122010005.

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This paper deals with a recent approximate analytical approach of the multistage optimal homotopy asymptotic method (MOHAM) for fractional optimal control problems (FOCPs). In this paper, FOCPs are developed in terms of a conformable derivative operator (CDO) sense. It is validated that the right CDO appears naturally in the formulation even when the system dynamics are described with the left CDO only. The CDO is employed to enlarge the stability region of the dynamical systems of the optimal control problems (OCPs). The necessary and transversal conditions are achieved using a Hamiltonian technique. The results demonstrated that as the fractional-order solution derivative tends to integer-order 1, the formulations lead to integer-order system solutions. Numerical results and a comparison with the exact solution and other approximate analytical solutions in fractional order are given to validate the efficiency of the MOHAM. Some numerical examples are included to demonstrate the effectiveness and applicability of the new technique.

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Rabiei, Faranak, Zeeshan Ali, Kamyar Hosseini, and M. M. Bhatti. "Optimal homotopy asymptotic method with Caputo fractional derivatives: a new approach for solving time-fractional Navier-Stokes equation." In Nanofluids. Elsevier, 2024. http://dx.doi.org/10.1016/b978-0-443-13625-2.00009-7.

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Conference papers on the topic "Optimal Homotopy Asymptotic Method (OHAM)"

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Marinca, Bogdan, and Ciprian Bogdan. "Optimal homotopy asymptotic method for a well-mixed SEIR model." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0163941.

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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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3

Ene, R. D., V. Marinca, R. Negrea, and B. Caruntu. "Optimal Homotopy Asymptotic Method for Solving a Nonlinear Problem in Elasticity." In 2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2012. http://dx.doi.org/10.1109/synasc.2012.12.

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Herisanu, Nicolae, and Vasile Marinca. "Optimal homotopy asymptotic method in the study of energy harvesting problems." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114302.

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Mabood, Fazle, Ahmad Izani Md Ismail, and Ishak Hashim. "Numerical solution of Painlev̀e equation I by optimal homotopy asymptotic method." In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801183.

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Ene, R. D., V. Marinca, and R. Negrea. "Optimal Homotopy Asymptotic Method for Viscous Boundary Layer Flow in Unbounded Domain." In 2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2014. http://dx.doi.org/10.1109/synasc.2014.22.

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Anakira, N. Ratib, A. K. Alomari, and I. Hashim. "Application of optimal homotopy asymptotic method for solving linear delay differential equations." In THE 2013 UKM FST POSTGRADUATE COLLOQUIUM: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2013 Postgraduate Colloquium. AIP Publishing LLC, 2013. http://dx.doi.org/10.1063/1.4858786.

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Anakira, Nidal. "Solution of system of ordinary differential equations by optimal homotopy asymptotic method." In SECOND INTERNATIONAL CONFERENCE OF MATHEMATICS (SICME2019). Author(s), 2019. http://dx.doi.org/10.1063/1.5097820.

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Nawaz, Rashid, and Laiq Zada. "Solving time fractional Sharma-Tasso-Olever equation by optimal homotopy asymptotic method." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043929.

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Marinca, Vasile, and Nicolae Herisanu. "Optimal homotopy asymptotic method for polytrophic spheres of the Lane-Emden type equation." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114303.

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