Solving certain classes of Lane-Emden type equations using the differential transformation method

In this paper, the differential transformation method (DTM) is applied to solve singular initial problems represented by certain classes of Lane-Emden type equations. Some new differential transformation formulas for certain exponential and logarithmic nonlinearities are derived. The approximate and...

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Bibliographic Details
Published in:Advances in difference equations 2012-10, Vol.2012 (1), p.1-11, Article 174
Main Authors: Khan, Yasir, Svoboda, Zdeněk, Šmarda, Zdeněk
Format: Article
Language:English
Subjects:
Accuracy
Analysis
Approximation
Difference and Functional Equations
Difference equations
Differential equations
Exact solutions
Functional Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
Progress in Functional Differential and Difference Equations
Transformations
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Summary:In this paper, the differential transformation method (DTM) is applied to solve singular initial problems represented by certain classes of Lane-Emden type equations. Some new differential transformation formulas for certain exponential and logarithmic nonlinearities are derived. The approximate and exact solutions of these equations are calculated in the form of series with easily computable terms. The results obtained with the proposed methods are in good agreement with those obtained by other methods. The advantages of this technique are shown as well.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/1687-1847-2012-174