AUTHORS: S. O. Edeki, A. Abolarinwa, P. O. Ogunniyi
Download as PDF
In this paper, natural transform combined with decomposition method is applied to the NewellWhitehead-Segel model for analytical solutions. For the purpose of illustration, examples on linear and nonlinear are considered. The results show efficiency, reliability, and simplicity of the proposed method. Hence, it is recommended for highly nonlinear differential models and systems
KEYWORDS: Analytical solutions; Decomposition Method; Newell-Whitehead-Segel model
REFERENCES:
[
1] P. Pue-on, Laplace Adomian Decomposition
Method for Solving Newell-Whitehead-Segel
Equation, Applied Mathematical Sciences, 7
(132), (2013), 6593-6600.
[2] A. Ghorbani and J. S. Nadjfi, He’s homotopy
perturbation method for calculating Adomian’s
polynomials, Int. J. Nonlin. Sci. Num. Simul. 8
(2) (2007), 229-332.
[3] J. Saberi-Nadjafi, A. Ghorbani, He’s homotopy
perturbation method: an effective tool for
solving nonlinear integral and integrodifferential equations, Computers &
Mathematics with Applications, 58,
(2009):1345–1351.
[4] J. Patade, and S. Bhalekar, Approximate
analytical solutions of Newell-WhiteheadSegel equation using a new iterative method,
World Journal of Modelling and Simulation, 11
(2), (2015): 94-103.
[5] M.M. Rashidi, The modified differential
transform method for solving MHD boundarylayer equations, Comput Phys Commun, 180,
(2009):2210–7.
[6] J. Singh, D. Kumar and S. Rathore, Application
of Homotopy Perturbation Transform Method
for Solving Linear and Nonlinear KleinGordon Equations, Journal of Information and
Computing Science, 7 (2), (2012): 131-139.
[7] A.M. Wazwaz, M.S. Mehanna, The combined
Laplace–Adomian method for handling
singular integral equation of heat transfer, Int J
Nonlinear Sci. 10 (2010): 248-52.
[8] S.O. Edeki, and G.O. Akinlabi, Coupled
method for solving time-fractional navier
stokes equation, International Journal of
Circuits, Systems and Signal Processing, 12
(2017), 27-34.
[9] J.H. He, Homotopy perturbation method: A
new nonlinear analytical technique, Appl.
Math. Comput. 135 (2003):73-79.
[10] G.O. Akinlabi and S.O. Edeki, On
Approximate and Closed-form Solution
Method for Initial-value Wave-like Models,
International Journal of Pure and Applied
Mathematics, 107(2), (2016): 449–456.
[11] S.O. Edeki, O.O. Ugbebor, and E.A. Owoloko,
He’s polynomials for analytical solutions of the
Black-Scholes pricing model for stock option
valuation, Proceedings of the World Congress
on Engineering 2016, Vol II, WCE 2016, June
29 - July 1, 2016, London, U.K.
[12] H.K. Mishra and A.K. Nagar, He-Laplace
Method for Linear and Nonlinear Partial
Differential Equations,” Journal of Applied
Mathematics, (2012), 1-16.
[13] S.O. Edeki, G.O. Akinlabi, and S. A. Adeosun,
On a modified transformation method for exact
and approximate solutions of linear
Schrödinger equations, AIP Conference
Proceedings 1705, 020048 (2016); doi:
10.1063/1.4940296.
[14] J.H. He, A coupling method of homotopy
techniques and perturbation technique for
nonlinear problems, International Journal of
Non-Linear Mechanics, 35(1) (2000): 37-43.
[15] S.O. Edeki, G.O. Akinlabi and S.A. Adeosun,
Analytic and Numerical Solutions of TimeFractional Linear Schrödinger Equation, Comm
Math Appl, 7 (1), (2016): 1–10.
[16] S.O. Edeki, O.P. Ogundile, B. Osoba, G.A.
Adeyemi, F.O. Egara, S.A. Ejoh, Coupled
FCT-HP for Analytical Solutions of the
Generalized Time-Fractional NewellWhitehead-Segel Equation, WSEAS
Transactions on Systems and Control, 13
(2018).
[17] S.A. Manaa, An Approximate solution to the
Newell-Whitehead-Segel equation by the
Adomian decomposition method, Raf. J. Comp.
Math. 8(1), (2011), 171-180.
[18] A. Aasaraai, Analytic solution for NewellWhitehead-Segel equation by differential
transform method, Middle-East J. Sci. Res. 10
(2), (2011), 270-273.
[19] A. Saravanan, N. Magesh, A comparison
between the reduced differential transform
method and the Adomian decomposition
method for the Newell- Whitehead-Segel
equation, J. Egyptian Math. Soc, 21 (2013),
259-265.
[20] J.E. Macias-Diaz, J. Ruiz-Ramirez, A nonstandard symmetry-preserving method to
compute bounded solutions of a generalized
Newell-Whitehead- Segel equation, Appl
Numer. Math, 61, (2011), 630-640.
[21] M.M.A. Mahgoub, Homotopy Perturbation
Method for Solving Newell-Whitehead-Segel
Equation, Advances in Theoretical and Applied
Mathematics, 11 (4), (2016): 399-406.
[22] G.O. Akinlabi, R.B. Adeniyi, E.A. Owoloko,
The solution of boundary value problems with
mixed boundary conditions via boundary value
methods, International Journal of Circuits,
Systems and Signal Processing, 12, (2018), 1-
6.
[23] M.M. Khader, On the numerical solutionsto
nonliear biochemical reaction model using
Picard-Pade technique, World Journal of
Modelling and Simulation, (2012) 38-46.
[24] G.O. Akinlabi, R.B. Adeniyi, E.A. Owoloko,
Hybrid boundary value methods for the
solution of first order stiff systems,
International Journal of Circuits, Systems and
Signal Processing, 11, (2017), 332-337.
[25] R. Mokhtari, A. S. Toodar and N. G. Chegini,
Application of the generalized differential
quadrature method in solving Burgers’
equations, Commun. Theor. Phys. 56 (6),
(2011), 1009.
[26] Z.H. Khan, W.A. Khan, N-Transform -
Properties and Applications, NUST Journal of
Engineering Sciences, 1 (1), (2008): 127-133.
[27] F.B.M. Belgacem and R. Silambarasan,
Theory of natural transform, Math. Eng. Sci.
Aerospace (MESA) 3 (1), (2012), 99-124.
[28] R. Silambarasan and F.B.M. Belgacem,
Applications of the Natural transform to
Maxwell’s equations, Progress of
Electromagnetic Research Symposium Proc.
Suzhou, China, (2011), 899-902.