Numerical analysis of high-order methods for variable-exponent fractional diffusion-wave equation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912606627823616 |
|---|---|
| author | Qiu, Wenlin Zheng, Xiangcheng |
| author_facet | Qiu, Wenlin Zheng, Xiangcheng |
| contents | This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this model is not available in the literature, partly because the variable-exponent Abel kernel in the leading term may not be positive definite or monotonic. We adopt the idea of model reformulation to obtain a more tractable form, which, however, still involves an ``indefinite-sign, nonpositive-definite, nonmonotonic'' convolution kernel that introduces difficulties in numerical analysis. We address this issue to design two high-order schemes and derive their stability and error estimate based on the proved solution regularity, with $α(0)$-order and second-order accuracy in time, respectively. Numerical experiments are presented to substantiate the theoretical findings and to show the transition behavior of the mechanical (diffusive) wave modeled by variable exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical analysis of high-order methods for variable-exponent fractional diffusion-wave equation Qiu, Wenlin Zheng, Xiangcheng Numerical Analysis 35R11, 65M12, 65M60 This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this model is not available in the literature, partly because the variable-exponent Abel kernel in the leading term may not be positive definite or monotonic. We adopt the idea of model reformulation to obtain a more tractable form, which, however, still involves an ``indefinite-sign, nonpositive-definite, nonmonotonic'' convolution kernel that introduces difficulties in numerical analysis. We address this issue to design two high-order schemes and derive their stability and error estimate based on the proved solution regularity, with $α(0)$-order and second-order accuracy in time, respectively. Numerical experiments are presented to substantiate the theoretical findings and to show the transition behavior of the mechanical (diffusive) wave modeled by variable exponent. |
| title | Numerical analysis of high-order methods for variable-exponent fractional diffusion-wave equation |
| topic | Numerical Analysis 35R11, 65M12, 65M60 |
| url | https://arxiv.org/abs/2406.02941 |