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Numerical analysis for compact difference scheme of fractional viscoelastic beam vibration models

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  • NSTL
  • Elsevier
In this article, a compact difference method is proposed for fractional viscoelastic beam vibration in stress-displacement form. The solvability, the unconditional stability and the convergence rates of second-order in time and fourth-order in space are rigorously proved for the fractional stress v and the displacement u, respectively, under a mild assumption on the loading f. Numerical experiments are given to verify the theoretic findings. One of the main contributions of this article is to evaluate the positive lower- and upper-bound of the eigenvalues of the Toeplitz matrix Lambda generated from the weighted Grunwald difference operator for fractional integral operators, and thus prove that the matrix Lambda is positive definite and can induce a norm in a vector space. This finding improves significantly the existing semi-positive definiteness theory of the matrix Lambda for fractional differential operators and facilitates the proof of the stability and convergence for the stress v. (C) 2022 Elsevier Inc. All rights reserved.

Fractional viscoelastic beam vibrationThe weighted Grunwald difference operatorFourth-order compact finite difference schemeLower and upper bounds of eigen valuesStability and convergence analysisSIMPLY SUPPORTED BEAMERROR ANALYSISALGORITHMCALCULUS

Li, Qing、Chen, Huanzhen

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Shandong Normal Univ

2022

10.1016/j.amc.2022.127146

Applied mathematics and computation

Applied mathematics and computation

EISCI
ISSN：0096-3003
年,卷(期)：2022.427
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