High order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates

Yan Jiang University of Science and Technology of China Chi-Wang Shu Brown University Mengping Zhang University of Science and Technology of China

Numerical Analysis and Scientific Computing mathscidoc:1610.25029

Mathematical Models and Methods in Applied Sciences, 25, 1553-1588, 2015
In this paper, we discuss high order finite difference weighted essentially non-oscillatory (WENO) schemes, coupled with total variation diminishing (TVD) Runge-Kutta (RK) temporal integration, for solving the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology. Since the solutions to this system are non-negative, we discuss a positivity-preserving limiter without compromising accuracy. Analysis is performed to justify the maintanance of third order spatial / temporal accuracy when the limiters are applied to a third order finite difference scheme and third order TVD-RK time discretization for solving this model. Numerical results are also provided to demonstrate these methods up to fifth order accuracy.
weighted essentially non-oscillatory scheme; high order accuracy; positivity-preserving; correlated random walk
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@inproceedings{yan2015high,
  title={High order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates},
  author={Yan Jiang, Chi-Wang Shu, and Mengping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012033121547988147},
  booktitle={Mathematical Models and Methods in Applied Sciences},
  volume={25},
  pages={1553-1588},
  year={2015},
}
Yan Jiang, Chi-Wang Shu, and Mengping Zhang. High order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates. 2015. Vol. 25. In Mathematical Models and Methods in Applied Sciences. pp.1553-1588. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012033121547988147.
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