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.
翻译:我们调查对齐坐标轴的平面圆形四边形的模型。 首先,我们开发一种分析方法,将这一问题降低到极点,并设计一种数字方法来查找附属参数。 这个方法使用Schwarz方程式来确定单位磁盘在特定圆形四边形上的一致映射。 我们还举了一个圆形四边形的例子,在这个圆形的圆形四边形中可以找到符合的模数值; 这个例子用来验证数字计算。 我们还使用另一种方法, 叫做 hpFEM, 用于计算元数。 这两个不同的方法提供了非常精确的结果 。