title: An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method.
abstract: 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.
authors.affiliation: Department of Mathematics, Ningbo University, Fenghua Road 818, Jiangbei District, Ningbo City, 315211 Zhejiang Province People's Republic of China.
authors.forename: Lie-Jun
authors.initials: LJ
authors.lastname: Xie
authors.affiliation: Department of Mathematics, Ningbo University, Fenghua Road 818, Jiangbei District, Ningbo City, 315211 Zhejiang Province People's Republic of China.
authors.forename: Cai-Lian
authors.initials: CL
authors.lastname: Zhou
authors.affiliation: Department of Mathematics, Ningbo University, Fenghua Road 818, Jiangbei District, Ningbo City, 315211 Zhejiang Province People's Republic of China.
authors.forename: Song
authors.initials: S
authors.lastname: Xu
keywords: Adomian polynomials; Approximate series solutions; Differential transform method; Improved differential transform method; Singular boundary value problem