# 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…

## One Citation

### Semi-implicit methods for advection equations with explicit forms of numerical solution

- Computer ScienceJapan Journal of Industrial and Applied Mathematics
- 2022

We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a…

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