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**A new algorithm for calculating one-dimensional differential transform of nonlinear functions.**
*(English)*
Zbl 1132.65062

Summary: A new technique for calculating the one-dimensional differential transform of nonlinear functions is developed. This new technique avoids the difficulties and massive computational work that usually arise from the standard method. The algorithm is illustrated by studying suitable forms of nonlinearity. Several nonlinear ordinary differential equations, including Troesch’s and Bratu-type problems, are then solved to demonstrate the reliability and efficiency of the proposed scheme. The present algorithm offers a computationally easier approach to compute the transformed function for all forms of nonlinearity. This gives the technique much wider applicability.

### MSC:

65L05 | Numerical methods for initial value problems involving ordinary differential equations |

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

34A34 | Nonlinear ordinary differential equations and systems |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

### Keywords:

differential transform method; nonlinear ordinary differential equation; Troesch’s problem; Bratu problem; numerical examples; algorithm
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\textit{S.-H. Chang} and \textit{I-L. Chang}, Appl. Math. Comput. 195, No. 2, 799--808 (2008; Zbl 1132.65062)

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### References:

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