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In this work, an effective numerical method is developed to solve a class ofsingular boundary value problems arising in various physical models by usingthe improved differential transform method (IDTM). The IDTM applies the Adomianpolynomials to handle the differential transforms of the nonlinearities arisingin the given differential equation. The relation between the Adomianpolynomials of those nonlinear functions and the coefficients of unknowntruncated series solution is given by a simple formula, through which one caneasily deduce the approximate solution which takes the form of a convergentseries. An upper bound for the estimation of approximate error is presented.Several physical problems are discussed as illustrative examples to testify thevalidity and applicability of the proposed method. Comparisons are made betweenthe present method and the other existing methods.

An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method