A multiscale Abel kernel and application in viscoelastic problem
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910712877547520 |
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| author | Qiu, Wenlin Guo, Tao Li, Yiqun Guo, Xu Zheng, Xiangcheng |
| author_facet | Qiu, Wenlin Guo, Tao Li, Yiqun Guo, Xu Zheng, Xiangcheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A multiscale Abel kernel and application in viscoelastic problem Qiu, Wenlin Guo, Tao Li, Yiqun Guo, Xu Zheng, Xiangcheng Numerical Analysis 45K05, 65M12, 65M60 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. |
| title | A multiscale Abel kernel and application in viscoelastic problem |
| topic | Numerical Analysis 45K05, 65M12, 65M60 |
| url | https://arxiv.org/abs/2411.16078 |