Please enter verification code
Confirm
Application of Laplace Variation Iteration Method to Solving the Nonlinear Gas Dynamics Equation
American Journal of Mathematical and Computer Modelling
Volume 5, Issue 4, December 2020, Pages: 127-133
Received: Sep. 11, 2020; Accepted: Oct. 19, 2020; Published: Dec. 16, 2020
Views 72      Downloads 37
Authors
Joseph Bonazebi Yindoula, Department of Exacts Sciences, Faculté des Sciences et Techniques, University Marien N’Gouabi, Brazzaville, Congo
Stevy Mikamona Mayembo, Department of Exacts Sciences, Faculté des Sciences et Techniques, University Marien N’Gouabi, Brazzaville, Congo
Gabriel Bissanga, Department of Exacts Sciences, Faculté des Sciences et Techniques, University Marien N’Gouabi, Brazzaville, Congo
Article Tools
Follow on us
Abstract
In this work, we use a new analytical technique called Laplace variational iteration method to construct the exact solution of the nonlinear equation of gas dynamics. This method is based on the determination of the Lagrange multiplier in an optimal way. Application of the method to three test modeling problems from mathematical physics leads to a sequence which tends towards the exact solution of the problem. The solution procedure shows the reliability of the method and is high accuracy evident.
Keywords
Laplace Variational Iteration Method, Nonlinear Gas Dynamics Equation, Lagrange Multiplier
To cite this article
Joseph Bonazebi Yindoula, Stevy Mikamona Mayembo, Gabriel Bissanga, Application of Laplace Variation Iteration Method to Solving the Nonlinear Gas Dynamics Equation, American Journal of Mathematical and Computer Modelling. Vol. 5, No. 4, 2020, pp. 127-133. doi: 10.11648/j.ajmcm.20200504.15
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
A. AL-Fayadh and H. Khawwan, Variational Iteration Transform Method for Solving Burger and Coupled Burger’s Equations, ARPN J. Eng. Appl. Sci., 12 (23): 6926-6932 (2017).
[2]
Shelu Maitama, Sabuwa Mustapha Kurawa, Zaria Road, An Efficient technique for solving gas dynamics equation using the Natural Decomposition Method. International Mathematical Furum, Vol. 9, 2014, n0. 24, 1177-1190.
[3]
Adesina. K.Adio, A Reliable technique for solving gas dynamics equation using Natural Homotopy Perturbation Method.Global journal of Science frontier. Research: Mathematics and Decission Sciences ISSN: 2249-4626 (2017).
[4]
JAGDEV SINGH, DEVENDRAKUMAR AND SUSHILA, Homotopy Perturbation Algorithm using Laplace Transform for gas dynamics equation, journal of the Applied Mathematics, Statistics and Informatics (JAMSI), 8 (2012) no 1.
[5]
OLAYIWOLA, M. O AKinpelu, F. O, Gbolagabe, A.W Modified Variational Iteration Method for the solution of nonlinear Partial Differential Equations. International Journal of Scienctific and Engineering Research volume 2, ISSN 10, oct-2011.
[6]
H. Aminikhah, A. Jamalian, Numerical Approximation for Nonlinear Gas Dynamic Equation, International journal of Partial Differential Equations, 2013 (2013), 1- 7. https://doi.org/10.1155/2013/846749.
[7]
Y. Keskin, G. Oturanc, Application of reduced Differential Transformation Method for solving Gas Dynamics Equation, International journal of Contemporary Mathematical Sciences, 5 (2010), no 22, 1091-1096.
[8]
D. J. Evans, H. Bulut, A new approach to the Gas dynamics equation: An application of the decomposition method, International Journal of Computer Mathematics, 79 (2002), no. 7, 817-822. https://doi.org/10.1080/00207160211297/846749.
[9]
Ali Al-Fayadh and Dina Saad Faraj, Combind Laplace transform-variational iteration method for sine-Gordon equation ISSN 1013-5316; CODEN: SINTE 8, SCi Int(Lahorc), 31 (1), 61-64-2019.
[10]
S. Saeedi, M .Mighani, An efficient technique in Finding the exact solutions for Cauchy problems Medbiotech Journal, MBTJ, 1 (3): 126-130, 2017. American Journal of Mathematical and Computer Modelling 2020; 5(4): 127-133 133
[11]
E. Hesameddini and H.Latifizadeh, Reconstruction of variational iteration algorithms using the Laplace transform, International Journal of nonlinear Sciences and Numerical Simulation, 10 (2009), 1377-1382.
[12]
ALI. AL-Fayadh, Approximate solution for Burger’s Fisherequationbyvariationaliterationtransformmethod. Tikrit Journal of Pure Science 23(8)2018.
[13]
J. H. He, X. H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons Fractals 29(1) (2006) 108-113.
[14]
Ji-Huan He, Xu-Hong Wu, Variational Iteration Method: New development and applications Computers and Mathematics with Applications 54(2007)881-894.
[15]
Ramezanpour, M., Montazerin, N., Izady, P., Doosthoseini, A., 2013. A new algorithm to solve the gas dynamic equation: An application of the Fourier Transform Adomian Decomposition Method. Applied Mathematical Sciences. 7(86), 4281-4286.
[16]
A. NIKKAR, A new Approach for solving Gas dynamic equation ACTA TECHNICA CORVINIENSIS-Bulletin of Engineering Tome V (Year 2012). Fascicule 4(oct- December) ISSN 2067-3809.
[17]
B Kumar Singh, P Kumar, Numerical Computation for Time-fractional Gas Dynamics Equations by Fractional Reduced Differential Transforms Method.
[18]
Jafari, H., Chun, C., Seifi, S., Saidy, M., 2009. Analytical solution for nonlinear Gas Dynamic equation by Homotopy Analysis Method. Application and Applied Mathematics. 4 (1), 149-154.
[19]
Rasulov, M., Karaguler, T., 2003. Finite difference schemes for solving system equations of gas dynamic in a class of discontinuous functions. Applied Mathematics and Computation. 143 (1), 145-164.
[20]
Keskin, Y., Oturanc, G., 2010. Application of Reduced Differential Transformation Method for solving Gas Dynamics Equation. International Journal of Contemporary Mathematical Sciences. 5 (22), 1091- 1096.
[21]
Nikkar, A., 2012. A new approach for solving gas dynamic equation. Acta Technica Corviniensis Bulletin of Engineering. 4, 113-116.
[22]
Jafari, H.,Zabihi, M., Saidy, M., 2008. Application of homotopy perturbation method for solving gas dynamic equation. Applied Mathematical Sciences. 2, 2393-2396.
[23]
Maitama, S., Sabuwa, M. K., 2014.An efficient Technique for solving Gas Dynamic Equation using the Natural Decomposition Method. International Mathematical Forum. 9 (24), 1177-1190.
[24]
Matinfar, M., Raeisi, Z., 2011. Variational Homotopy perturbation Method for solving the nonlinear Gas Dynamics Equation. International journal of Mathematical Modelling & Computations. 1 (3), 183- 187.
[25]
Jafari, H., Hosseinzadeh, S., and Salehpoor, E., 2008. “A new approach to gas dynamics equation: Application of variational iteration method”. Applied Mathematical Sciences, vol. 2, pp. 2397-2400.
[26]
Maitama, S., Sabuwa, M. K., 2014.An efficient Technique for solving Gas Dynamic Equation using the Natural Decomposition Method. International Mathematical Forum. 9 (24), 1177-1190.
[27]
Matinfar, M., Raeisi, Z., 2011. Variational Homotopy perturbation Method for solving the nonlinear Gas Dynamics Equation.International journal of Mathematical Modelling & Computations. 1 (3), 183- 187.
[28]
Mohiuddin, G., 2015. Modified Homotopy perturbation Method (MHPM) for Dynamics Gas Equation. Mathematical Theory and Modelling. 5 (6), 173-175.
[29]
Singh, J., Kumar, D., Sushila., 2012. Homotopy perturbation Algorithm using Laplace Transform for Gas Dynamics Equation. Journal of the Applied Mathematics, Statistics and Informatics (JAMSI), 8 (1), 55-61.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186