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Ebaid, Abd Elhalim

A reliable aftertreatment for improving the differential transformation method and its application to nonlinear oscillators with fractional nonlinearities. (English) Zbl 1221.34009

Commun. Nonlinear Sci. Numer. Simul. 16, No. 1, 528-536 (2011).
Summary: A new aftertreatment technique is developed in this paper to deal with the truncated series derived by the differential transformation method (DTM) to obtain approximate periodic solutions. The proposed aftertreatment technique splits into two types, named as (Sine-AT technique, SAT) and (Cosine-AT technique, CAT). It is shown that the differential transformation method with the proposed aftertreatment technique is very effective and convenient for a class of nonlinear oscillatory problems with fractional nonlinearities without any need for Padé approximants or Laplace transform.

Cited in 12 Documents

MSC:

34A08 Fractional ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations

Keywords:

Duffing-harmonic oscillator; relativistic harmonic oscillator; periodic solutions; differential transformation method; aftertreatment technique
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\textit{A. E. Ebaid}, Commun. Nonlinear Sci. Numer. Simul. 16, No. 1, 528--536 (2011; Zbl 1221.34009)
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References:

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