Numerical solution of time fractional Kuramoto-Sivashinsky equation by Adomian decomposition method and applications
Downloads
DOI:
https://doi.org/10.26637/MJM0803/0060Abstract
In the paper, we develop the Adomian Decomposition Method for fractional order nonlinear Kuramoto-Sivashinsky (KS) equation. Caputo fractional derivatives are used to define fractional derivatives. We know that KS equation has many applications in physical phenomenon such as reaction diffusion system, long waves on the boundary of two viscous fluids and hydrodynamics. In this paper, we will solve time fractional KS equation which may help to researchers for their work. We solve some examples numerically, which will show the efficiency and convenience of Adomian Decomposition Method.
Keywords:
Kurmoto-Sivashinsky equation, Fractional derivative, Adomian Decomposition Method, Convergence, MathematicaMathematics Subject Classification:
Mathematics- Pages: 1078-1084
- Date Published: 01-07-2020
- Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
I. Podlubny, Fractional Differential equations Academic Press, San Diago, (1999).
S. Jogdand, S. Kulkarni and K.C.Takale, Error Analysis of solution of time fractional convection diffusion equation, JETIR, 6(3)(2019), 1-12.
J. Biazar and E. Babolian, Solution of the system of ordinary differential equations by Adomian Decomposition Method, Appl. Math. Comput., 147(3)(2004), 713-719.
H. Jafari, Solving a system of nonlinear fractional differential equations using Adomian Decomposition, Journal of Computational and Applied Mathematics, 196(2006), 644-651.
M. Lakestani and M. Dehghan, Numerical Solutions of the generalised KuramotoSivashinsky equation using B- spline functions, Applied Mathematical Modelling, $36(2012), 605-617$
D. Anders, M. Dittmann, A higher-order finite element approach to the KuramotoSivashinsky equation, ZAMM. Z. Angew Math. Mech., 92(2012), 599-607.
M. Raissi and G. E. Karniadakis, Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations, Division of Applied Mathematics, Brown University, Providence, RI, 2912, USA, Journal of Computational Physics, (2017).
M. G. Porshokouhi and B. Rahimi, Application of Homotopy Perturbation Method for solution of KuramotoSivashinsky equation, International Mathematical Forum, $6(45)(2011), 2225-2230$.
M. G. Porshokouhi, Application of He's VIM for solution of the family of KuramotoSivashinsky equation, Journal of King Saud University Science, 23(2011), 407-411.
H. Lai and C. Ma, Lattice Boltzmann method for the generalized KuramotoSivashinsky equation, PhysicaA : Statistical Mechanics and its applications, 388(8)(2009), $1405-1412$.
S.A.Manna and F. H.Easif, ADM for solving the KuramotoSivashinsky equation, IOSR Journal of Mathematics, 10(1)(2014), 08-12.
W. Yin, F. Xu, Asymptotic Expansion of the Solutions to Time-Space Fractional Kuramoto-Sivashinsky equation,Hindawi Publishing Corporation Advances in Mathematical Physics, (2016), 12-20.
C. T. D. Tchaho, J. R. Bogning, Modulated Soliton Solution of the modified Kuramoto-Sivashinsky equations, American Journal of Computational and Applied Mathematics, 2(5)(2012), 218-224.
N. A. Kudryashov and M. B. Soukharev, Popular ansatz methods and solitary waves solutions of KuramotoSivashinsky equations, Hindawi Publishing Corporation Advances in Mathematical Physics, (2016), 12 pages.
S. Momani, Z. Odibat, Analytical solutions of a time fractional Navier-Stokes equation by Adomian decomposition method, Appl. Math. Comput. , 177(2)(2006), 488-494.
S. Saha Ray, New Approach for General Convergence of the ADM, World Applied Sciences Journal, 32 (11)(2014), 2264-2268.
- NA
Similar Articles
- M. Sebasti Jeya Pushpam, N. Rajesh, On faintly \(b-\mathscr{I}\)-continuous multifunctions , Malaya Journal of Matematik: Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
- M. Sebasti Jeya Pushpam, N. Rajesh, On slightly \(b-\mathscr{I}\)-continuous multifunctions , Malaya Journal of Matematik: Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
