期刊
SPRINGERPLUS
卷 5, 期 -, 页码 -出版社
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1186/s40064-016-2753-9
关键词
Singular boundary value problem; Differential transform method; Adomian polynomials; Improved differential transform method; Approximate series solutions
资金
- Scientific Research Fund of Zhejiang Provincial Education Department of China [Y201430940]
- K.C. Wong Magna Fund in Ningbo University
In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinearities arising in the given differential equation. The relation between the Adomian polynomials of those nonlinear functions and the coefficients of unknown truncated series solution is given by a simple formula, through which one can easily deduce the approximate solution which takes the form of a convergent series. An upper bound for the estimation of approximate error is presented. Several physical problems are discussed as illustrative examples to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods.
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