三元扩散模型关于小参数的渐近展开方法
Asymptotic Expansion Method with Respect to Small Parameter for Ternary Diffusion Models.
作者信息
Danielewski Marek, Leszczyński Henryk, Szafrańska Anna
机构信息
Faculty of Materials Science and Ceramics, AGH University of Science and Technology, 30 Mickiewicza Av., 30-059, Krakow, Poland.
Institute of Mathematics, University of Gdańsk, Wit Stwosz Street 57, 80-952, Gdańsk, Poland.
出版信息
Interdiscip Sci. 2017 Sep;9(3):423-433. doi: 10.1007/s12539-017-0228-5. Epub 2017 Apr 12.
Ternary diffusion models lead to strongly coupled systems of PDEs. We choose the smallest diffusion coefficient as a small parameter in a power series expansion whose components fulfill relatively simple equations. Although this series is divergent, one can use its finite sums to derive feasible numerical approximations, e.g. finite difference methods (FDMs).
三元扩散模型会导致强耦合的偏微分方程组。我们在幂级数展开中选择最小的扩散系数作为小参数，其各项满足相对简单的方程。尽管这个级数是发散的，但可以用其有限和来推导可行的数值近似，例如有限差分法（FDMs）。
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