The Zhou’s Method for Solving the Euler Equidimensional Equation
Abstract: In this work, we apply the Zhou’s method [1] or differential transformation method (DTM) for solving the Euler equidimensional equation. The Zhou’s method may be considered as alternative and efficient for finding the approximate solutions of initial values problems. We prove superiority of this method by applying them on the some Euler type equation, in this case of order 2 and 3 [2]. The power series solution of the reduced equation transforms into an approximate implicit solution of the original equations. The results agreed with the exact solution obtained via transformation to a constant coefficient equation.
Cite this paper: Alzate, P. , Salazar, J. and Varela, C. (2016) The Zhou’s Method for Solving the Euler Equidimensional Equation. Applied Mathematics, 7, 2165-2173. doi: 10.4236/am.2016.717172.
References

[1]   Zhou, J.K. (1986) Differential Transformation and Its Applications for Electrical Circuits. Huazhong University Press, Wuhan.

[2]   Odibat, Z. (2008) Differential Transform Method for Solving Volterra Integral Equations with Separable Kernels. Mathematical and Computer Modelling, 48, 1144-1146.
http://dx.doi.org/10.1016/j.mcm.2007.12.022

[3]   Shawagfeh, N. and Kaya, D. (2004) Comparing Numerical Methods for Solutions of Ordinary Differential Equations. Applied Mathematics Letters, 17, 323-328.
http://dx.doi.org/10.1016/S0893-9659(04)90070-5

[4]   Ardila, W. and Cárdenas, P. (2013) The Zhou’s Method for Solving White-Dwarfs Equation. Applied Mathematics, 10C, 28-32.

[5]   Arikoglu, O. (2006) Solution of Difference Equations by Using Differential Transform Method. Applied Mathematics and Computational, 173, 126-136.

[6]   Cárdenas, P. and Arboleda, A. (2012) Resolución de ecuaciones diferenciales no lineales por el método de transformación diferencial. Universidad Tecnológica de Pereira, Colombia. Tesis de Maestría en Matemáticas.

[7]   Cárdenas, P. (2012) An Iterative Method for Solving Two Special Cases of Lane-Emden Type Equations. American Journal of Computational Mathematics, 4, 242-253.

Top