Numerical Solution of Kawahara Equation Using Neural Network
Keywords:
Kawahara Equation, Modified Kawahara Equation, Artificial Neural NetworkAbstract
An artificial neural network technique is proposed in this research to solve the well-known partial differential equations of the types: Kawahara and modified Kawahara equations. The mathematical model of the equation was developed with the help of artificial neural networks. The construction requires imposing certain constrains on the values of the input, bias and output weights, and on the attribution of certain roles of each aforementioned parameters. The results obtained from the proposed technique were very accurate, simple and convenient. Moreover, the comparison between the approximated solutions and the exact one has done. This comparison found them in a good agreement with each other due to of superior properties of the Neural Network.
References
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A. Junaid, M. A. Z. Raja, and I. M. Qureshi, Evolutionary Computing Approach for the Solution of Initial value Problems in Ordinary Differential Equations, World Academy of Science, Engineering and Technology (55) 2009.
A. Malek and R. S. Beidokhti, Numerical solution for high order differential equations using a hybrid neural network Optimization method, Applied Mathematics and Computation, 183(2006), 260-271.
A. S. Yilmaz and Z. Ozer, Pitch angle control in wind turbines above the rated wind speed by multi-layer perceptron and Radial basis function neural networks, Expert Systems with Applications, 36(6) (2009), 9767–9775.
D. T. Pham, E. Koc, A. Ghanbarzadeh and S. Otri, Optimization of the weights of multi-layered perceptron's using the bees algorithm, Proc. 5thInternational Symposium on Intelligent Manufacturing Systems. Turkey, May 2006, 38–46.
D. T. Pham and X. Liu, Neural Networks for Identification, Prediction and Control,. Springer Verlag, London. 1995.
H. A . Jalab, Rabha W. Ibrahim, Shayma A. Murad, Amera I. Melhum, and S. B.Hadid, Numerical Solution of Lane-Emden Equation Using Neural Network, International Conference on Fundamental and Applied Sciences 2012, AIP Conf. Proc. 1482, 414-418 (2012); doi: 10.1063/1.4757505 © 2012 American Institute of Physics .
Kawahara T, Oscillatory solitary waves in dispersive media, Journal of the physical society of Japan, 1972; 33: pp.260-264.
M. Ghalambaz, A.R. Noghrehabadi, M.A. Behrang, E. Assareh, A. Ghanbarzadeh and N. Hedayat, A Hybrid Neural Network and Gravitational Search Algorithm (HNNGSA) Method to Solve the well-known Wessinger's Equation, World Academy of Science, Engineering and Technology 73, 2011.
M. Kurulay , Approximate analytic solutions of the modified Kawahara equation with homotopy analysis method , Advances in Difference Equations 2012, 2012: 178 doi:10.1186/1687-1847-2012-178. 1-7.
N. A. Kudryashov, New exact solutions for the Kawahara equation using Exp-function method, arXiv:1004.1049v1 [nlin.SI] 7 Apr 2010.
Sirendaoreji, New exact travelling wave solutions for the Kawahara and modified Kawahara equations, Chaos Solutions Fractals 19 (2004) 147–150.
S.Suresh, S.N.Omkar,andV.Mani,"Parallel Implementationof Back-
PropagationAlgorithmin Networks ofWorkstations", IEEETransactionsOn
ParallelAndDistributed Systems,Vol.16,No.1, January2005.
Sh. Bahzadi, Convergence of iterative methods for solving Kawahara equation, International Journal of the Physical Sciences Vol. 6(33),9 December, 2011. pp. 7512 – 7523.
V. G. Gupta and S. Gupta, A Reliable Algorithm for Solving Non-Linear
Kawahara Equation and its Generalization, International Journal of Computational Science and Mathematics, Volume 2, Number 3 (2010), pp.407- 416.
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Published
2014-06-30
How to Cite
Murad, S. A., Melhum, A. I., & Omar, L. A. (2014). Numerical Solution of Kawahara Equation Using Neural Network. Science Journal of University of Zakho, 2(1), 196–203. Retrieved from https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/153
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