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arXiv · 2411.16078

A multiscale Abel kernel and application in viscoelastic problem

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.

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Wenlin Qiu, Tao Guo, Yiqun Li, Xu Guo, Xiangcheng Zheng. 2024-11-25. A multiscale Abel kernel and application in viscoelastic problem. https://arxiv.org/abs/2411.16078

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