A new method based on generalized Taylor expansion for computing a series solution of the linear systems

Toutounian, Faezeh; Nasabzadeh, Hamideh

doi:10.1016/j.amc.2014.10.003

Cited by 2 publications

(3 citation statements)

References 9 publications

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“…Moreover, the Taylor-like method [11] is an arbitrary high order A-stable method that avoids extremely small stepsizes during the integration procedure. To avoid the analytical computation of the successive derivatives involved in the Taylor-like methods, numerical differentiation [21,22], automatic differentiation [23], differential transformation [24][25][26] and Infinity Computer with a new numeral system [27][28][29][30][31][32] can be used. In fact, Taylor-like explicit methods [5,7,[9][10][11] have computational drawbacks with zero-component derivative or zero-vector norm in their component or vector forms, respectively.…”

Section: Introductionmentioning

confidence: 99%

A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations

2019

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A new generalised Taylor-like explicit method for stiff ordinary differential equations (ODEs) is proposed. The algorithm is presented in its component and vector forms. The error and stability analysis of the method are developed showing that it has an arbitrary high order of convergence and the L-stability property. Moreover, it is verified that several integration schemes are special cases of the new general form. The method is applied on stiff problems and the numerical solutions are compared with those of the classical Taylor-like integration schemes. The results show that the proposed method is accurate and overcomes the shortcoming of the classical Taylor-like schemes in their component and vector forms.

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Section: Introductionmentioning

confidence: 99%

A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations

2019

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“…Taylor formula [16,17], as an indispensable math tool in mathematical analysis, plays a key role on approximate calculation. It aims to transform a complex function into a concise polynomial function on the premise of maintaining a high approximation precision.…”

Section: Introductionmentioning

confidence: 99%

“…Δ depends on the frequency of the excitation. In this work the excitation frequency is 20 Hz, so Δ = 0.05 s.(ii) Compute matricesA 1 , A 2 , A , A V , A , B 1 , B 2 , B , B V , B , C 1 , C 2 , C , C V, and C in(16),(17), and (18).…”

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confidence: 99%

Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method

Li¹,

Deng

2016

Shock and Vibration

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A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white noise excitation are applied on a cantilever beam, respectively, to illustrate the effectiveness of this algorithm. One also makes a comparison between the new method and conventional state space method. The results show that the proposed method can obtain a more accurate identified force time history whether the responses are polluted by noise or not.

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A new method based on generalized Taylor expansion for computing a series solution of the linear systems

Cited by 2 publications

References 9 publications

A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations

A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations

Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method

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