The particular solutions of some types of EulerCauchy ODE using the differential transform method
Volume 12, Issue 3, pp 146151
http://dx.doi.org/10.22436/jnsa.012.03.02
Publication Date: November 30, 2018
Submission Date: July 21, 2018
Revision Date: August 09, 2018
Accteptance Date: September 22, 2018

3399
Downloads

2627
Views
Authors
Meshari Alesemi
 Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia.
M. A. ElMoneam
 Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia.
Bader S. Bader
 Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia.
E. S. Aly
 Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia.
Abstract
In this paper, we apply the differential transform method to find the
particular solutions of some types of EulerCauchy ordinary differential
equations. The first model is a special case of the nonhomogeneous \(n^{\rm th}\) order ordinary differential equations of EulerCauchy equation. The
second model under consideration in this paper is the nonhomogeneous second
order differential equation of EulerCauchy equation with a bulge function.
This study showed that this method is powerful and efficient in finding the
particular solution for EulerCauchy ODE and capable of reducing the size of
calculations comparing with other methods.
Share and Cite
ISRP Style
Meshari Alesemi, M. A. ElMoneam, Bader S. Bader, E. S. Aly, The particular solutions of some types of EulerCauchy ODE using the differential transform method, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 3, 146151
AMA Style
Alesemi Meshari, ElMoneam M. A., Bader Bader S., Aly E. S., The particular solutions of some types of EulerCauchy ODE using the differential transform method. J. Nonlinear Sci. Appl. (2019); 12(3):146151
Chicago/Turabian Style
Alesemi, Meshari, ElMoneam, M. A., Bader, Bader S., Aly, E. S.. "The particular solutions of some types of EulerCauchy ODE using the differential transform method." Journal of Nonlinear Sciences and Applications, 12, no. 3 (2019): 146151
Keywords
 Differential equations
 differential transform method
 EulerCauchy equations
MSC
References

[1]
M. S. Abdualrab, A formula for solving a special case of EulerCauchy ODE., Int. Math. Forum, 4 (2009), 1997–2000.

[2]
J. Ali , One dimensional differential transform method for some higher order boundary value problems in finite domain, Int. J. Contemp. Math. Sci., 7 (2012), 263–272.

[3]
M. T. Alquran, Applying differential transform method to nonlinear partial differential equations: a modified approach, Appl. Appl. Math., 7 (2012), 155–163.

[4]
A. Aslanov, Determination of convergence intervals of the series solutions of EmdenFowler equations using polytropes and isothermal spheres, Phy. Lett. A, 372 (2008), 3555–3561.

[5]
K. Batiha, B. Batiha, A new algorithm for solving linear ordinary differential equations, World Appl. Sci. J., 15 (2011), 1774–1779.

[6]
C. Bervillier, Status of the differential transformation method, Appl. Math. Comput., 218 (2012), 10158–10170.

[7]
J. Biazar, M. Eslami, Differential transform method for quadratic Riccati differential equation, Int. J. Nonlinear Sci., 9 (2010), 444–447.

[8]
S.H. Chang, I.L. Chang, A new algorithm for calculating one dimensional differential transform of nonlinear functions, Appl. Math. Comput., 195 (2008), 799–805.

[9]
E. A. Elmabrouk, F. Abdewahid, Useful Formulas for Onedimensional Differential Transform, Britsh J. Appl. Sci. Tech., 18 (2016), 1–8.

[10]
V. S. Ert ürk, Application of differential transformation method to linear sixthorder boundary value problems, Appl. Math. Sci. (Ruse), 1 (2007), 51–58.

[11]
V. S. Ertürk, Approximate Solutions of a Class of Nonlinear Differential Equations by Using Differential Transformation Method, Int. J. Pure Appl. Math., 30 (2006), 403–407.

[12]
G. G. Ev Pukhov, Differential transforms and circuit theory, Circuit Theory Appl., 10 (2008), 265–276.

[13]
B. Ghil, H. Kim, The Solution of EulerCauchy Equation Using Laplace Transform, Int. J. math. Anal., 9 (2015), 2611–2618.

[14]
P. Haarsa, S. Pothat , The Reduction of Order on CauchyEuler Equation with a Bulge Function, Appl. Math. Sci., 9 (2015), 1139–1143.

[15]
I. H. A. H. Hassan, V. S. Ertürk, Solution of differential types of the linear and nonlinear higherorder boundary value problems by differential transformation method, Eur. J. Pure Appl. Math., 2 (2009), 426–447.

[16]
K. Parand, Z. Roozbahani, F. Bayat Babolghani, Solving nonlinear LaneEmden type equations with unsupervised combined artificial neural networks, Int. J. Industrial Mathematics, 5 (2013), 12 pages.

[17]
M. A. Soliman, Y. AlZeghayer, Aproximate analytical solution for the isothermal Lane Emden equation in a spherical geometry, Revist Mexicanade Astronmiay Atrofisca, 15 (2015), 173–180.

[18]
A.M. Wazwas, A new algorithm for solving differential equations of LaneEmden type, Applied Math. Comput., 118 (2001), 287–310.

[19]
A.M. Wazwas, The modified decomposition method for analytic treatment of differential equations, Appl. Math. Comput., 173 (2006), 165–176.

[20]
A. Yildrim, T. Özis, Solutions of singular IVPs of LaneEmden type by the variational iteration method, Nonlinear Anal., 70 (2009), 2480–2484.

[21]
E. M. E. Zayed, M. A. ElMoneam, Some oscillation criteria for second order nonlinear functional ordinary differential equations, Acta Math. Sci. Ser. B (Engl. Ed.), 27 (2007), 602–610.

[22]
E. M. E. Zayed, S. R. Grace, H. ElMetwally, M. A. ElMoneam, The oscillatory behavior of second order nonlinear functional differential equations, Arab. J. Sci. Eng. Sect. A Sci., 31 (2006), 23–30.

[23]
J. K. Zhou, Differential transformation and its applications for electrical circuits, Huarjung University Press, wuuhahn (1986)