Efficient Scaling and Moving Techniques for Spectral Methods in Unbounded Domains

@article{Xia2021EfficientSA,
  title={Efficient Scaling and Moving Techniques for Spectral Methods in Unbounded Domains},
  author={Mingtao Xia and Sihong Shao and Tom Chou},
  journal={SIAM J. Sci. Comput.},
  year={2021},
  volume={43},
  pages={A3244-A3268}
}
When using Laguerre and Hermite spectral methods to numerically solve PDEs in unbounded domains, the number of collocation points assigned inside the region of interest is often insufficient, particularly when the region is expanded or translated to safely capture the unknown solution. Simply increasing the number of collocation points cannot ensure a fast convergence to spectral accuracy. In this paper, we propose a scaling technique and a moving technique to adaptively cluster enough… Expand

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