Numerical Solution of a Class of Nonlinear Emden-Fowler Equations by Using Differential Transform Method

Anahtar Kelimeler:

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Numerical Solution of a Class of Nonlinear Emden-Fowler Equations by Using Differential Transform Method

In this paper, approximate and/or analytical solutions of the Emden-Fowler type equations in the secondorder ordinary differential equations are obtained by applying differential transformation method (DTM). In this work, two examples are given and DTM yields solutions in convergent series forms with easily computable terms by using a reliable algorithm and in most cases iterations leads to the high accuracy of the solutions. Comparisons with the analytical solutions and the solutions found by the DTM show the efficiency in solving equations with singularity. In fact, the numerical results reveal that DTM is very efficient, reliable and accurate

Keywords:

Nonlinear differential equations, Singular initial value problems, Differential transform method, Emden-Fowler equations Numerical solution,

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S. Chandrasekhar, Introduction to the Study of Stellar Structure, Dover Publications, New York, 1967.
H. T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, 1962.
O. U. Richardson, the Emission of Electricity from Hot Bodies, Longman, Green and Co., London, 1921.
M. S. H. Chowdhury, I. Hashim, Solutions of Emden-Fowler Equations by homotopy- perturbation Method, Nonlinear Analysis: Real Word Applications, 10 (2009) 104-115.
J. K. Zhou, Differential Transformation and its Applications for Electrical Circuits, Huazhong University Press, Wuhan, P. R. China (1986), In Chinese.
A. Arikoglu, I. Ozkol, Solution of difference equations by using differential transform method, Applied Mathematics and Computation, 174 (2006) 1216-1228.
F. Ayaz, Solutions of the system of differential equations by differential transform method, Applied Mathematics and Computation, 147 (2004) 547-567.
C. L. Chen, Y. C. Liu, Solutions of two-boundary-value problems using the differential transform method, Journal of Optimization Theory and Application, 99 (1998) 23-35.
I. H. Abdel-Halim Hassan, differential transform technique for solving higher order initial value problems, Applied Mathematics and Computation, 154 (2004) 299-311.
C. K. Chen, S. S. Chen, Application of the differential transform method to a non-linear conservative system, Applied Mathematics and Computation 154 (2004) 431-441.
C. W. Bert, H. Zeng, Analysis of axial vibration of compound bars by differential transform method, Journal of Sound and Vibration, 275 (2004) 641-647.
B. L. Kuo, Applications of the differential transform method to the solutions of the free convection problem, Applied Mathematics and Computation 165 (2005) 63-79.
L. M. Berkovich, The Generalized Emden-Fowler Equation, Symmetry in Nonlinear Mathematical Physics, V. 1, (1997), 155-163.