A Semi-Analytical Method for The Solution of Linear And Nonlinear Newell-Whitehead-Segel Equations
The aim of this work is to use a semi-analytical method “Reduced Differential Transform Method (RDTM)” for the solution of linear and nonlinear Newell-Whitehead-Segel Equations (NWSE). RDTM does not require linearization, transformation, discretization, perturbation or restrictive assumptions. To determine the performance measure of the RDTM, two illustrative examples were considered. The comparative study of the results obtained via the RDTM was compared with that of the exact solution. Hence, RDTM offers solutions with easily computable components as convergent series and is an alternative approach that overcomes the shortcoming of complex calculations of differential transform method.
 Bahşi, K. and Yalçinbaş, S., A new algorithm for the numerical solution of telegraph equations by using Fibonacci polynomials. Mathematical and Computational Application. 21(2016) 1-12.
 Fadugba, S.E. and Owoeye, K.O., Reduced Differential Transform for Solving Special Linear and Nonlinear Partial Differential Equations, International Journal of Engineering and Future Technology, Vol. 16, No. 3, (in Press, 2019), Abu Dhabi, UAE.
 He, J.H., A new approach to nonlinear partial differential equations, Commun. Nonlinear Sci. Numer. Simul. 2(1997) 203-205.
 He, J.H., Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput. 135(2003) 73-79.
 He, J.H. and Wu, X.H., Exp-function method for nonlinear wave equations, Chaos Solitons Fract. 30(2006) 700-708.
 Keskin, Y. and Oturanç, G., The reduced differential transform method for partial differential equations, Int. J. Nonlin. Sci. Numer. Simul. 10(2009) 741-749.
 Keskin, Y. and Oturanç, G., The reduced differential transform method for solving linear and nonlinear wave equations, Iran. J. Sci. Technol. 34(2010) 113-122.
 Li, Q., Zheng, Z. and Liu, J., Lattice Boltzmann model for nonlinear heat equations, Adv. Neural Netw. (2012) 140-148.
 Servi, S., Keskin, Y. and Oturanç, G., Reduced differential transform method for improved Boussinesq equation, AIP Conference Proceedings 1648, 370012 (2015).
 Srivastava, V.K., Mukesh, K.A. and Chaurasia, R.K., Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraphic equations, J. King Saud Univ. Eng. Sci. 17(2014).
 Zhang, J.L., Wang, M.L. and Fang, Z.D., The improved F-expansion method and its applications, Phys. Lett. A. 350(2006) 103-109.
 Zhou, J.K., Differential transformation and its application for electrical circuits, Huazhong University Press, Wuhan, China, 1986.
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