An adaptive algorithm for efficient computation of level curves of surfaces

Breda, Dimitri; Maset, Stefano; Vermiglio, Rossana

doi:10.1007/s11075-009-9303-2

Cited by 16 publications

(15 citation statements)

References 10 publications

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“…see [31]). Efficiency could also be increased if non-uniform grid is used in the parameter plane (for such methods see [32] and [33]). The convergence of the rightmost characteristic exponents were investigated for parameter combinations given in Table 1.…”

Section: Resultsmentioning

confidence: 99%

A pseudospectral tau approximation for time delay systems and its comparison with other weighted‐residual‐type methods

Lehotzky

Insperger

2016

Numerical Meth Engineering

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This paper presents a method which applies pseudospectral tau approximation for retarded functional differential equations (RFDEs). The goal is to construct a system of ordinary differential equations (ODEs), which provides a finite dimensional approximation of the original RFDE. The method can be used to determine approximate stability diagrams for RFDEs. Thorough numerical case studies show that the rightmost characteristic roots of the ODE approximation converge to the rightmost characteristic roots of the original RFDE. Application of the method to time-periodic RFDEs is also demonstrated, and the convergence of the stability boundaries is verified numerically. The method is compared with recently developed highly efficient numerical methods: the pseudospectral collocation (also called Chebyshev spectral continuous-time approximation), the spectral Legendre tau method and the spectral element method. The comparison is based on the stability analysis of three linear autonomous RFDEs. The efficiency of the methods is measured by the convergence rate of stability boundaries in the space of system parameters, by the convergence rate of the rightmost characteristic exponent and by the computation time of the stability charts.

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Section: Resultsmentioning

confidence: 99%

A pseudospectral tau approximation for time delay systems and its comparison with other weighted‐residual‐type methods

Lehotzky

Insperger

2016

Numerical Meth Engineering

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“…Thereafter, the approximate border of stability is obtained as a level curve of this 3-dimensional surface at 1. Note that the efficiency of this method can be increased if system parameters are computed sparsely far from the boundary of stability and with an increasing density close to the boundary of stability (for such methods see [7] and [4]). …”

Section: General Settingsmentioning

confidence: 99%

Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays

Lehotzky

Insperger

Stépàn

2016

Communications in Nonlinear Science and Numerical Simulation

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“…As outlined in [6], the algorithm of Matlab contour function is relatively simple. It is based on covering the region of interest by a uniform grid of points.…”

Section: Mapping the Zero Level Curvesmentioning

confidence: 99%

QPmR - Quasi-Polynomial Root-Finder: Algorithm Update and Examples

Vyhlídal

Zı́tek

2014

Delay Systems

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Abstract. An updated QPmR algorithm implementation for computation and analysis of the spectrum of quasi-polynomials is presented. The objective is to compute all the zeros of a quasi-polynomial located in a given region of the complex plane. The root-finding task is based on mapping the quasi-polynomial in the complex plane. Consequently, utilizing spectrum distribution diagram of the quasipolynomial, the asymptotic exponentials of the retarded chains are determined. If the quasi-polynomial is of neutral type, the spectrum of associated exponential polynomial is assessed, supplemented by determining the safe upper bound of its spectrum. Next to the outline of the computational tools involved in QPmR, its Matlab implementation is presented. Finally, the algorithm is demonstrated by three examples.

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An adaptive algorithm for efficient computation of level curves of surfaces

Cited by 16 publications

References 10 publications

A pseudospectral tau approximation for time delay systems and its comparison with other weighted‐residual‐type methods

A pseudospectral tau approximation for time delay systems and its comparison with other weighted‐residual‐type methods

Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays

QPmR - Quasi-Polynomial Root-Finder: Algorithm Update and Examples

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