Publication detail

Numerical Inversion of 3D Laplace Transforms for Weakly Nonlinear Systems Solution

BRANČÍK, L.

Original Title

Numerical Inversion of 3D Laplace Transforms for Weakly Nonlinear Systems Solution

English Title

Numerical Inversion of 3D Laplace Transforms for Weakly Nonlinear Systems Solution

Type

conference paper

Language

en

Original Abstract

The paper deals with a technique for numerical inversion of three-dimensional Laplace transforms (3D NILT) being based on the FFT & IFFT in conjunction with the quotient-difference algorithm. This method generalizes 2D NILT technique developed formerly to three variables. Especially an error analysis has resulted in a new formula equating a relative error of the method to paths of the integration of triple Bromwich integral. To evaluate triple infinite sums obtained by numerical integration, the partial inversion technique is used. The method was algorithmized in Matlab language environment and applied for solving a response of a weakly nonlinear circuit via Volterra series expansion to demonstrate its practical usefulness.

English abstract

The paper deals with a technique for numerical inversion of three-dimensional Laplace transforms (3D NILT) being based on the FFT & IFFT in conjunction with the quotient-difference algorithm. This method generalizes 2D NILT technique developed formerly to three variables. Especially an error analysis has resulted in a new formula equating a relative error of the method to paths of the integration of triple Bromwich integral. To evaluate triple infinite sums obtained by numerical integration, the partial inversion technique is used. The method was algorithmized in Matlab language environment and applied for solving a response of a weakly nonlinear circuit via Volterra series expansion to demonstrate its practical usefulness.

Keywords

Numerical inversion, three-dimensional Laplace transform, weakly nonlinear system, Volterra series.

RIV year

2010

Released

19.04.2010

Publisher

Brno University of Technology

Location

Brno, Czech Republic

ISBN

978-1-4244-6319-0

Book

Proceedings of 20th International Conference RADIOELEKTRONIKA 2010

Pages from

221

Pages to

224

Pages count

4

URL

BibTex


@inproceedings{BUT29366,
  author="Lubomír {Brančík}",
  title="Numerical Inversion of 3D Laplace Transforms for Weakly Nonlinear Systems Solution",
  annote="The paper deals with a technique for numerical inversion of three-dimensional Laplace transforms (3D NILT) being based on the FFT & IFFT in conjunction with the quotient-difference algorithm. This method generalizes 2D NILT technique developed formerly to three variables. Especially an error analysis has resulted in a new formula equating a relative error of the method to paths of the integration of triple Bromwich integral. To evaluate triple infinite sums obtained by numerical integration, the partial inversion technique is used. The method was algorithmized in Matlab language environment and applied for solving a response of a weakly nonlinear circuit via Volterra series expansion to demonstrate its practical usefulness.",
  address="Brno University of Technology",
  booktitle="Proceedings of 20th International Conference RADIOELEKTRONIKA 2010",
  chapter="29366",
  howpublished="electronic, physical medium",
  institution="Brno University of Technology",
  year="2010",
  month="april",
  pages="221--224",
  publisher="Brno University of Technology",
  type="conference paper"
}