• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1265-1277
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• 2009

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.767-777
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• 2007

By proving a summation formula, we enumerate the expansions for the mock theta functions of order 2 in terms of partial mock theta functions of order 2, 3 and 6. We show a relation between Ramanujan's ${\mu}(q)$-function and his sixth order mock theta functions. In addition, we also give the continued fraction representation for ${\mu}(q)$ and 2nd order mock theta functions and $Pad\acute{e}$ approximants.

• Journal of Electrical Engineering and Technology
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• v.11 no.3
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• pp.618-628
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• 2016

Active power filter (APF) has been proved as a flexible solution for compensating the harmonic distortion caused by nonlinear loads in power distribution power systems. Digital repetitive control can achieve zero steady-state error tracking of any periodic signal while the sampling points within one repetitive cycle must be a known integer. However, the compensation performance of the APF would be degradation when the grid frequency varies. In this paper, an improved repetitive control scheme with frequency adaptive capability is presented to track any periodic signal with variable grid frequency, where the variable delay items caused by time-varying grid frequency are approximated with Pade approximants. Additionally, the stability criterion of proposed repetitive control scheme is given. A three-phase shunt APF experimental platform with proposed repetitive control scheme is built in our laboratory. Simulation and experimental results demonstrate the effectiveness of the proposed repetitive control scheme.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.299-304
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• 1996

This paper studies the rational approximation of multiple input delay systems using the Hankel singular values and vectors, which are the soultion of a transcendental equation. Rational approximatants are obtained from output normal realizations which are constructed by the Hankel singular values and vectors. Consequently, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pade approximants.