Volume 68 | Issue 2 | Year 2022 | Article Id. IJMTT-V68I2P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I2P520
In this paper we are studying importance of Homotopy Perturbation Method. To check the efficacy of this method three problem of Partial Differential Equation (PDE) will be solved using HPM. The numerical results shall prove that this method is a useful and impressive for explanation of PDE and advantageousness of the new capability. The HPM is defined as a new idea, new developments techniques certainly provided the conclusion.
[1] J. H. He, Homotopy Perturbation Tchnique, Computer Methods in Applied Mechanics and Engineering, 178 (1999) 257.
[2] J .H. He, A coupling method of a Homotopy technique and a perturbation technique for nonlinear problems, Int. J. Non-Linear Mech. 35(1) (2000) 37.
[3] J. H. He, The Homotopy perturbation method for non linear oscillators with discontinuities, Appl. Math. Comput. 151(1) (2004) 287.
[4] Ji-Huan He, Recent Development of the Homotopy Perturbation Method, Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder 31(2008) 205.
[5] T. Zhanlav, O. Chuluunbaatar V. Ulziibayar, Higher-Order Numerical Solution of Two-Dimensional Coupled Burger's Equations, American Journal of Computational Mathematics, 6 (2016)120.
[6] Suleman M. Qingbiao W. Ghulam A. Approximate analytic solution of (2 + 1) dimensional coupled differential Burger's equation using Elzaki Homotopy Perturbation Method, Alexandria Engineering Journal 55 (2016)1817.
[7] Fatima. N, Homotopy Perturbation Method for Solving Boussinesq and Fishers Type Equation, Published in Proceedings Second (IEEE) International Conference on Computational Intelligence & Communication Technology, (2016).
[8] Mohammed M., Tarig M. E., Some systems of nonlinear partial differential equations by using Adomian and modified decomposition methods, African Journal of Mathematics and Computer Science Research, 7 (2014) 61-67.
[9] Monika Dhariwal & Nahid Fatima, Comparison of Homotopy Perturbation Method with New Homotopy Perturbation Method, @ 2019SUSCOM, Hosting by Elsevier SSRN (2019) 2272.
[10] Nahid Fatima & Sunita Daniel, Solution of Wave Equations and Heat Equations using HPM, Applied Mathematics and Scientific Computing, © Springer Nature Switzerland AG, 1 (2019) 367.
[11] Nahid Fatima & Monica Dhariwal, Solution of nonlinear Coupled Burger and linear Burgers equation, International Journal of Engineering & Technology UAE, 7(2018) 670.
[12] Nahid Fatima, The Study of Heat Conduction Equation by Homotopy Perturbation Method. SN Computer Science, 3 (2022) 65.
[13] Nahid Fatima & Monika Dhariwal, Solutions of Differential Equations for Prediction of COVID-19 Cases by Homotopy Perturbation Method,Taylor & Francis Group Chapter in Intelligent Computing Applications for COVID-19, 1 (2021)17.
[14] Liao, S.J. (1992). The proposed homotopy analysis technique for the solution of linear problems. Ph.D. Thesis, Shanghai Jiao Tong University.
[15] Ji-Huan He, Xu-Hong Wu, Variational iteration method: New development and applications, science direct, Computers and Mathematics with Applications, 54 (2007) 881–894.
[16] Gupta, Neelam and Kanth, Neel Study of heat flow in a rod using homotopy analysis method and homotopy perturbation method Cite as: AIP Conference Proceedings 2061, 020013 (2019). https://doi.org/10.1063/1.5086635Published Online: 10 January 2019
[17] Xiao-Xia Li1 and Chunhui He1,2, Homotopy perturbation method coupled with the enhanced perturbation method Journal of Low Frequency Noise, Vibration and Active Control ,The Author(s), 0(0) (2018) 1-5. DOI: 10.1177/1461348418800554 journals.sagepub.com/home/lfn.
[18] A.-M. Wazwaz, A reliable technique for solving the wave equation in an infinite one-dimensional medium, Applied Mathematics and Computation, 92(1) (1998) 1–7.
[19] A.-M. Wazwaz, Adomian decomposition method for a reliable treatment of the Bratu-type equations, Applied Mathematics and Computation, 166(3) (2005) 652–663.
[20] Musa Rahamh Gad-Allah a & Tarig M. Elzaki b, An Application of improvement of New Homotopy Perturbation Method for Solving Third Order Nonlinear Singular Partial Differential Equations,ISSN 2456-1312, Universal Journal of Mathematics,2(1).
[21] Mohammed M., Tarig M. E., A study some systems of nonlinear partial differential equations by using Adomian and modified decomposition methods, African Journal Of Mathematics And Computer Science Research, 7 (2014) 61-67.
[22] Dan-Ni Yu, Ji-Huan He, Andres G Garcıa First, Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators Published November 18, (2018). Collection https://doi.org/10.1177/1461348418811028
[23] Yue Wua, Ji-Huan Heb, Homotopy perturbation method for nonlinear oscillators with coordinate dependent mass, Results in Physics, 10 (2018) 270-271
[24] N Fatima; Solution of gas dynamic and wave equations with VIM Advances in Fluid Dynamics, (2021).
[25] Ji-Huan He, Recent Development of The Homotopy Perturbation Method, Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center, 31 (2008) 205–209.
Nahid Fatima, "Higher order Burgers and Non Linear Equation with Different Boundary Condition by HPM," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 2, pp. 133-140, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I2P520