On a numerical algorithm for the solution of the radial Loewner equation
On a numerical algorithm for the solution of the radial Loewner equation
复制标题
求解径向Loewner方程的数值算法
DOI：
10.1002/mma.4640
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Hirokazu Shimauchi
中科院分区：
文献类型：
--
作者：
Ikkei Hotta;Hirokazu Shimauchi
Loewner偏微分方程提供了单位圆盘上的单参数共形映射族。这些图像描述了复平面上扩展单连通域的流动，称为Loewner流。本文提出了一种求解径向Loewner偏微分方程的数值算法。将该算法应用于Loewner流动的可视化中，取得了良好的效果和精度.从理论的角度来看，我们的算法是基于一个递归公式，用于确定多项式近似的系数。我们证明了每个系数收敛到真值具有合理的规律性。
The Loewner partial differential equation provides a one‐parametric family of conformal maps on the unit disk. The images describe a flow of an expanding simply‐connected domain, called the Loewner flow, on the complex plane. In this paper, we present a numerical algorithm for solving the radial Loewner partial differential equation. The algorithm is applied to visualization of Loewner flows with the performance and precision. From the theoretical point of view, our algorithm is based on a recursive formula for determining coefficients of polynomial approximations. We prove that each coefficient converges to true values with reasonable regularity.