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Mathematics > Numerical Analysis

arXiv:2411.16078 (math)
[Submitted on 25 Nov 2024]

Title:A multiscale Abel kernel and application in viscoelastic problem

Authors:Wenlin Qiu, Tao Guo, Yiqun Li, Xu Guo, Xiangcheng Zheng
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Abstract:We consider the variable-exponent Abel kernel and demonstrate its multiscale nature in modeling crossover dynamics from the initial quasi-exponential behavior to long-term power-law behavior. Then we apply this to an integro-differential equation modeling, e.g. mechanical vibration of viscoelastic materials with changing material properties. We apply the Crank-Nicolson method and the linear interpolation quadrature to design a temporal second-order scheme, and develop a framework of exponentially weighted energy argument in error estimate to account for the non-positivity and non-monotonicity of the multiscale kernel. Numerical experiments are carried out to substantiate the theoretical findings and the crossover dynamics of the model.
Subjects: Numerical Analysis (math.NA)
MSC classes: 45K05, 65M12, 65M60
Cite as: arXiv:2411.16078 [math.NA]
  (or arXiv:2411.16078v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2411.16078

Submission history

From: Wenlin Qiu [view email]
[v1] Mon, 25 Nov 2024 04:09:20 UTC (295 KB)
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