• Corpus ID: 234741722

Positivity preservation of implicit discretizations of the advection equation

@article{Hadjimichael2021PositivityPO,
  title={Positivity preservation of implicit discretizations of the advection equation},
  author={Yiannis Hadjimichael and David I. Ketcheson and Lajos L'oczi},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.07403}
}
We analyze, from the viewpoint of positivity preservation, certain discretizations of a fundamental partial differential equation, the one-dimensional advection equation with periodic boundary condition. The full discretization is obtained by coupling a finite difference spatial semi-discretization (the secondand some higher-order centered difference schemes, or the Fourier spectral collocation method) with an arbitrary θ-method in time (including the forward and backward Euler methods, and a… 

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