Numerical Methods for a Class of Reaction-Diffusion Equations With Free Boundaries
@inproceedings{Liu2019NumericalMF,
title={Numerical Methods for a Class of Reaction-Diffusion Equations With Free Boundaries},
author={Shuang Liu},
year={2019}
}The spreading behavior of new or invasive species is a central topic in ecology. The modelings of free boundary problems are widely studied to better understand the nature of spreading behavior of new species. From mathematical modeling point of view, it is a challenge to perform numerical simulations of free boundary problems, due to the moving boundary, the stiffness of the system and topological changes. In this work, we design numerical methods to investigate the spreading behavior of new…
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2 Citations
Numerical Methods for a Two-Species Competition-Diffusion Model with Free Boundaries
- Physics
- 2018
A front tracking method coupled with an implicit solver for the 1D model and a level set approach to handle the moving boundaries to efficiently treat complicated topological changes are introduced.
Integration factor combined with level set method for reaction-diffusion systems with free boundary in high spatial dimensions
- Computer Science, MathematicsArXiv
- 2022
This paper rewrite all ETD schemes into a linear combination of specific φ -functions and apply one start-of-the-art algorithm to compute the matrix-vector multiplications, which provides computational advantages with adaptive Krylov subspaces and extends this method by incorporating the level set method to solve the free boundary problem.
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