Multivariate polynomial interpolation and meshfree differentiation via undetermined coefficients

Belley, Jean-Marc; Belley, P.; Day, Alexandre G. R.

doi:10.1016/j.cam.2012.09.012

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…For fractional order systems, the existing analytical methods include Green function method, 17 Adomian decomposition method, 18 Homotopy perturbation method, 19 Homotopy analysis method, 20 and variational iteration method. 21 In addition, some scholars have also adopted undetermined coefficient method, 22,23 method of direct partition of motions, 24 multi-scale method, 25,26 and average method 27 to solve some special vibration systems. As one of them, the average method can realize the characteristics of simple understanding and high accuracy in solving fractional order dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of fractional oscillator system with cosine excitation utilizing the average method

Xie

Wang

Chen

et al. 2022

Math Methods in App Sciences

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In this paper, an analytical and numerical algorithm for solving displacement response of fractional oscillator system with cosine excitation is established. The analytical method is to solve steady‐state response and transient response solutions of the system by means of average method and then the total displacement response solution is the sum of steady‐state solution and transient solution. The numerical method is to use the Grünwald–Letnikov definition of fractional derivatives to discretize the fractional differential term in the system and then to reduce the order of the original system. Then, the approximate response solution of the system under the general periodic excitation is obtained by using the Fourier series expansion method and the superposition principle of linear system. Finally, the effectiveness and feasibility of the analytical technique are verified by numerical simulation, and the influence of fractional order, linear damping coefficient and fractional derivative coefficient on the amplitude of the steady‐state response and the total displacement response of the system is analyzed.

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Section: Introductionmentioning

confidence: 99%

Dynamical analysis of fractional oscillator system with cosine excitation utilizing the average method

Xie

Wang

Chen

et al. 2022

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

A family of multivariate multiquadric quasi-interpolation operators with higher degree polynomial reproduction

2015

Journal of Computational and Applied Mathematics

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Dynamic Pricing and Risk Analytics Under Competition and Stochastic Reference Price Effects

2016

IEEE Trans. Ind. Inf.

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Multivariate polynomial interpolation and meshfree differentiation via undetermined coefficients

Cited by 3 publications

References 9 publications

Dynamical analysis of fractional oscillator system with cosine excitation utilizing the average method

Dynamical analysis of fractional oscillator system with cosine excitation utilizing the average method

A family of multivariate multiquadric quasi-interpolation operators with higher degree polynomial reproduction

Dynamic Pricing and Risk Analytics Under Competition and Stochastic Reference Price Effects

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