A fast algorithm to compute the steady-state solution of nonlinear circuits by piecewise linearization

Herdem, Saadetdin; Köksal, Mustafa Serdar

doi:10.1016/s0045-7906(00)00046-x

Cited by 8 publications

(3 citation statements)

References 14 publications

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“…The latter approach is less complicated because the procedures operate directly in the time domain, and the Fourier series representations are not used. There are also other methods which reduce the problem to linear and small-signals analysis (Herdem and Koksal, 2002), combining numerical integration with boundary-value problems and the waveform-relaxation method (Lelarasmee et al , 1982; Caron et al , 2016, 2017).…”

Section: Introductionmentioning

confidence: 99%

Discrete differential operators for periodic and two-periodic time functions

Sobczyk

Radzik

Radwan-Pragłowska

2019

COMPEL

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Purpose To identify the properties of novel discrete differential operators of the first- and the second-order for periodic and two-periodic time functions. Design/methodology/approach The development of relations between the values of first and second derivatives of periodic and two-periodic functions, as well as the values of the functions themselves for a set of time instants. Numerical tests of discrete operators for selected periodic and two-periodic functions. Findings Novel discrete differential operators for periodic and two-periodic time functions determining their first and the second derivatives at very high accuracy basing on relatively low number of points per highest harmonic. Research limitations/implications Reduce the complexity of creation difference equations for ordinary non-linear differential equations used to find periodic or two-periodic solutions, when they exist. Practical implications Application to steady-state analysis of non-linear dynamic systems for solutions predicted as periodic or two-periodic in time. Originality/value Identify novel discrete differential operators for periodic and two-periodic time functions engaging a large set of time instants that determine the first and second derivatives with very high accuracy.

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Section: Introductionmentioning

confidence: 99%

Discrete differential operators for periodic and two-periodic time functions

Sobczyk

Radzik

Radwan-Pragłowska

2019

COMPEL

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“…The latter are less complicated because they operate directly in the time domain. There exist other methods reducing the problem to linear one [28,29] or combining the numerical integration with boundary value problems, like the waveform relaxation method [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Sobczyk,

Radzik

2018

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This paper investigates an algorithm for finding steady-states in electromechanical systems for the cases of their periodic nature. The algorithm enables to specify the steady-state solution identified directly in time domain. The basis for such an algorithm is a discrete differential operator that specifies the values of the first derivative of the periodic function in the selected set of points on the basis of the values of that function in the same set of points. It creates algebraic equations describing the steady-state solution for the nonlinear differential equations describing electromechanical systems. In this paper, the direct time-domain approach is tested for the simple converter considering. The algorithm used in this paper is competitive with respect to the one known in literature an approach based on the harmonic balance method operated in frequency domain.

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“…In fact, piecewise linearization is a more efficient tool for finding approximate solutions. Some researchers have used piecewise linearization in applications [5] [6]. Also, some researchers have used piecewise linearization to solve ODEs and PDEs [7].…”

Section: Introductionmentioning

confidence: 99%

The Best Piecewise Linearization of Nonlinear Functions

Mazarei¹,

Behroozpoor²,

Kamyad³

2014

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In this paper, we propose a method for finding the best piecewise linearization of nonlinear functions. For this aim, we try to obtain the best approximation of a nonlinear function as a piecewise linear function. Our method is based on an optimization problem. The optimal solution of this optimization problem is the best piecewise linear approximation of nonlinear function. Finally, we examine our method to some examples.

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A fast algorithm to compute the steady-state solution of nonlinear circuits by piecewise linearization

Cited by 8 publications

References 14 publications

Discrete differential operators for periodic and two-periodic time functions

Discrete differential operators for periodic and two-periodic time functions

Bulletin of the Polish Academy of Sciences: Technical Sciences

The Best Piecewise Linearization of Nonlinear Functions

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