solving Kuramoto–Sivashinsky equation by the New iterative method and estimate the optimal parameters by using pso algorithm

karam Abed

Abstract


In this study, optimal parameters estimation is performed for non-linear (Kuramoto-Sivashinsky) equation using a crossbred method between Particle swarm optimization (PSO) algorithm and (NIM) technique and for the appropriateness we call it (PSO-NIM). It turns out that the optimal parameters significantly improve the solutions when we use a fitness function suitable for the issue. The results confirmed that the get approximate solutions are in suitable pact with the exact solutions and the proposed method provides high accuracy and efficiency in comparison with (NIM) which use traditionally chosen parameters.


References


Majeed A. Yousif, Fadhil Easif, Saad A. Manaa, "Solving the Kuramoto-Sivashinsky equation via Variational Iteration Method", 3 (3) pp:260-264, 2014.

John Wiley and Sons, "partial differential equation", 2007.

A. A. Hemeda, “New iterative method: application to the nth order integro-differential equations”, Information B, vol. 16, no. 6, pp. 3841-3852, 2013.

S. Bhalekar and V. Daftardar-Gejji. “Convergence of the new iterative method”, International Journal of Differential Equations, 2011.

A. Hemeda and M. Saleh Alluhaibi. “New iterative method for solving gas dynamic equation”, International Journal of Applied Mathematical Research, 3(2):190–195, 2014.

I. Podlubny, Fractional Differential Equations, Academic Press, New York, NY, USA, 1999.

K. Al-Khaled and S. Momani, “An approximate solution for a fractional diffusion-wave equation using the decomposition method,” Applied Mathematics and Computation, vol. 165, no. 2, pp. 473–483, 2005.

A. Hanyga, “Multidimensional solutions of time-fractional diffusion-wave equations,” The Royal Society of London A, vol. 458, no. 2020, pp. 933–957, 2002.

V.Daftardar-Gejji andH. Jafari, “An iterative method for solving nonlinear functional equations,” Journal of Mathematical Analysis and Applications, vol. 316, no. 2, pp.753–763, 2006.

A. A. Hemeda, “New iterative method: application to the nthorder integro- differential equations,” Information B, vol. 16, no. 6, pp. 3841–3852, 2013.

S. Bhalekar and V. Daftardar-Gejji, “New iterative method: application to partial differential equations,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 778– 783, 2008.

Manoj Kumar, Anuj Shanker Saxena, “new iterative method for solving higher order Kdv equations”,4th international conference on science, technology and management, India international Centre, New Delhi, (ICSTM-16), 15 May 2016, www.conferenceworld,in, Isbn;978-81-932074-8-2.

Dongshu Wang · Dapei Tan1 · Lei Liu, "Particle swarm optimization algorithm: an overview", pp:387–408, 2018.

Chong Tian1, Chunshan Xue, Yongfeng Cui,"Application of Partial Differential Equation Based on PSO Algorithm ", ISSN: 1473-804x online, 1473-8031 print.

G. I. Sivashinsky, “Nonlinear analysis of hydrodynamic instability in laminar flames I: Derivation of basic equations”, Acta Astronau, 4, (1977), pp. 1177-1206.

Y. Kuramoto, “Diffusion-induced chaos in reaction systems”, Suppl. Prog. Theor. Phys, 64, (1978), pp. 346-367.

Z. Sh. Al-Talib, S. F. AL-Azzawi, “Projective and Hybrid Projective Synchronization of 4-D Hyperchaotic System Via Nonlinear Controller Strategy,” TELKOMNIKA Telecommunication, Computing, Electronics and Control, vol. 18, No 2, April 2020.

S. Y. Al-hayali and S. F. AL-Azzawi, “An Optimal Control for Complete Synchronization of 4D Rabinovich Hyperchaotic Systems,” TELKOMNIKA Telecommunication, Computing, Electronics and Control vol. 18, no 2, pp. 994-1000, Apr 2020.

A. S. Al-Obeidi and S. F. Al-Azzawi, “Chaos Synchronization in a 6-D Hyperchaotic System with Self-Excited Attractor,” TELKOMNIKA Telecommunication, Computing, Electronics and Control, vol. 18, No 3, June 2020.

S. Al-hayali and S. F. AL-Azzawi, “An Optimal Control for Complete Synchronization of 4D Rabinovich Hyperchaotic Systems,” vol. 18, No 2, April 2020.

S. F. Al-Azzawi and M. M. Aziz, “Chaos Synchronization of Nonlinear Dynamical Systems via a Novel Analytical Approach,” Alexandria Engineering Journal, vol. 57, no. 4, pp. 3493-3500, Dec 2018.

S. F. Al-Azzawi and M. M. Aziz, “Strategies of Linear Feedback Control and its classification,” TELKOMNIKA Telecommunication, Computing, Electronics and Control, vol. 17, no. 4, pp. 1931-1940, Aug 2019.

S. Al-hayali, S. F. AL-Azzawi, “An Optimal Nonlinear Control for Anti-Synchronization of Rabinovich Hyperchaotic System,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 19, no. 1, July 2020.

Muhammet Kurulay, Aydin Secer and Mehmet Ali Akinlar, "A New Approximate Analytical Solution of Kuramoto –Sivashinsky Equation Using Homotopy Analysis Method", Applied Mathematics & Information Sciences, No. 1, 267-271 2013.

Akrivis, Georgios, Smyrlis, Yiorgos-sokratis, Implicit-explicit BDF methods for the Kuramoto-Sivashinsky equation, Appl. Numer. Math. 51, 2004, 151–169.

Uddin, M., Haq, S., Siraj-ul-Islam, A mesh-free numerical method for solution of the family of Kuramoto–Sivashinsky equations, Appl. Math. Comput. 212, 2009, 458–469.

Brajesh Kumar Singh, Geeta Arora, Pramod Kumar, "A note on solving the fourth-order Kuramoto-Sivashinsky equation by the compact finite difference scheme", Ain Shams Engineering Journal, pp: 1581–1589, 2018.

A. S. Al-Obeidi and S. F. Al-Azzawi, “Projective Synchronization for a Class of 6-D Hyperchaotic Lorenz System,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 16, no. 2, pp. 692-700, Nov 2019.

K. A. Abed & A. A. Ahmad, “The Best Parameters Selection Using Pso Algorithm to Solving For Ito System by New Iterative Technique,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 18, no. 3, pp. 1638-1645, June 2020.

Z. N. Al-kateeb and M. R. Al-Bazaz, “Steganography in Colored Images Based on Biometrics,” Tikrit Journal of Pure Science, vol. 24, no. 3, pp. 111-117, May 2019.

A.F., Qasim, B.J. Salim, "Application New Iterative Method for Solving Modified Korteweg-Devries (MKdV) System from Three Equations" Journal of Advanced Research in Dynamical and Control Systems, vol.11 pp.1-7, 2019.

A. S. Al-Obeidi and S. F. Al-Azzawi, “Chaos Synchronization in a 6-D Hyperchaotic System with Self-Excited Attractor,” TELKOMNIKA Telecommunication, Computing, Electronics and Control, vol. 18, no 3, June 2020.

M. A. A. Alhafedh and O. S. Qasim, "Two-Stage Gene Selection in Microarray Dataset Using Fuzzy Mutual Information and Binary Particle Swarm Optimization," Indian Journal of Forensic Medicine & Toxicology, vol. 13,pp. 1162-1171, 2019.




DOI: http://doi.org/10.11591/ijeecs.v19.i2.pp%25p
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