An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method
| Autor: | Lie-jun Xie, Song Xu, Cai-lian Zhou |
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| Rok vydání: | 2016 |
| Předmět: |
Mathematical optimization
Differential equation 010103 numerical & computational mathematics 02 engineering and technology Differential transform method Adomian polynomials 01 natural sciences Singular solution FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Applied mathematics Mathematics - Numerical Analysis Boundary value problem 0101 mathematics Mathematics Multidisciplinary Singular boundary value problem Research Numerical analysis 020206 networking & telecommunications Numerical Analysis (math.NA) Singular boundary method Improved differential transform method Nonlinear system Approximate series solutions Spectral method Adomian decomposition method |
| Zdroj: | SpringerPlus |
| ISSN: | 2193-1801 |
| DOI: | 10.1186/s40064-016-2753-9 |
| Popis: | 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. 21 pages, 4 figures |
| Databáze: | OpenAIRE |
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