论文标题
与尖尖的对称圆形四边形的共形模量
Conformal Moduli of Symmetric Circular Quadrilaterals With Cusps
论文作者
论文摘要
我们研究了平面圆形四边形的模量相对于两个坐标轴对称。首先，我们开发了一种分析方法，该方法将这个问题减少到ODES并设计了一种数字方法来找出附件参数。该方法使用Schwarz方程来确定单位磁盘上的共形映射到给定的四边形上。我们还举例说明了一个圆形四边形的示例，可以在分析形式中找到共形模量的值。此示例用于验证数字计算。我们还使用另一种称为HPFEM的方法进行模量的数字计算。这两种不同的方法提供了与高精度一致的结果。
We investigate moduli of planar circular quadrilaterals symmetric with respect to both the coordinate axes. First we develop an analytic approach which reduces this problem to ODEs and devise a numeric method to find out the accessory parameters. This method uses the Schwarz equation to determine conformal mapping of the unit disk onto a given circular quadrilateral. We also give an example of a circular quadrilateral for which the value of the conformal modulus can be found in the analytic form; this example is used to validate the numeric calculations. We also use another method, so called hpFEM, for the numeric calculation of the moduli. These two different approaches provide results agreeing with high accuracy.
