  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.
