Publication detail

Elaboration of FFT-based 2D-NILT Methods in Terms of Accuracy and Numerical Stability

BRANČÍK, L.

Original Title

Elaboration of FFT-based 2D-NILT Methods in Terms of Accuracy and Numerical Stability

English Title

Elaboration of FFT-based 2D-NILT Methods in Terms of Accuracy and Numerical Stability

Type

journal article

Language

en

Original Abstract

Laplace transforms in two variables can very be useful for solving certain partial differential equations, namely those describing transient behaviour of linear dynamical systems. In practice, it is often either too difficult or even impossible to obtain corresponding originals by analytic methods. In such cases methods that enable getting original numerically have to be applied. The 2D-NILT method based on FFT, recently published and verified in Matlab language, seems be well usable. Its main advantage lies in high speed of calculation, however, it is necessary to connect it always with proper technique of acceleration of the convergence to achieve required accuracy. It was shown either the epsilon or the quotient-difference algorithms are very suitable for this purpose. In the paper an error analysis, comparison and estimation of the optimal 2D-NILT parameters are newly presented.

English abstract

Laplace transforms in two variables can very be useful for solving certain partial differential equations, namely those describing transient behaviour of linear dynamical systems. In practice, it is often either too difficult or even impossible to obtain corresponding originals by analytic methods. In such cases methods that enable getting original numerically have to be applied. The 2D-NILT method based on FFT, recently published and verified in Matlab language, seems be well usable. Its main advantage lies in high speed of calculation, however, it is necessary to connect it always with proper technique of acceleration of the convergence to achieve required accuracy. It was shown either the epsilon or the quotient-difference algorithms are very suitable for this purpose. In the paper an error analysis, comparison and estimation of the optimal 2D-NILT parameters are newly presented.

Keywords

two-dimensional Laplace transform, numerical inversion, FFT, epsilon algorithm, quotient-difference algorithm

RIV year

2005

Released

01.02.2005

Publisher

SIGMA-NOT

Pages from

84

Pages to

89

Pages count

6

BibTex


@article{BUT42759,
  author="Lubomír {Brančík}",
  title="Elaboration of FFT-based 2D-NILT Methods in Terms of Accuracy and Numerical Stability",
  annote="Laplace transforms in two variables can very be useful for solving certain partial differential equations, namely those describing transient behaviour of linear dynamical systems. In practice, it is often either too difficult or even impossible to obtain corresponding originals by analytic methods. In such cases methods that enable getting original numerically have to be applied. The 2D-NILT method based on FFT, recently published and verified in Matlab language, seems be well usable. Its main advantage lies in high speed of calculation, however, it is necessary to connect it always with proper technique of acceleration of the convergence to achieve  required accuracy. It was shown either the epsilon or the quotient-difference algorithms are very suitable for this purpose. In the paper an error analysis, comparison and estimation of the optimal 2D-NILT parameters are newly presented.",
  address="SIGMA-NOT",
  chapter="42759",
  institution="SIGMA-NOT",
  journal="Przeglad Elektrotechniczny",
  number="2",
  volume="LXXXI",
  year="2005",
  month="february",
  pages="84",
  publisher="SIGMA-NOT",
  type="journal article"
}