计算力学学报2012，Vol.29Issue(1)：38-42,5.
在Cap—cyclide坐标中Wangerin函数Nm^n（v）的高精度数值计算
The high precision numerical calculation of Wangerin function Nm^n（v） based on Cap-cyclide coordinates
黄华 1恰汗·合孜尔 1宋艳萍 1努尔古丽·艾力1
作者信息
- 1. 新疆农业大学数理学院,乌鲁木齐830052
- 折叠
摘要
Abstract
In Cap-cyclide coordinates, the Wangerin function Nm^n（v）, which is eigenvalue function, includes complete elliptic integral of the first kind and Jacobi elliptic functions. To get the high precision numerical solutions of Wangerin function Nm^n（v）, firstly, the iterative method is applied to take numerical calculation in complete elliptic integral of the first kind. The numerical results are as accurate as theoretic values. Secondly, we carry on numerical calculation with the identical equations of Jacohi elliptic functions, and the number of numerical solutions~ significant digits is up to 14. Then, based on these results, we procure the high precision numerical solutions of Wangerin function Nm^n（v） upon these two steps. The result provides the theoretical basis for further research on convergence and stability of Wan- gerin function Nm^n（v）, and shows that it is very useful to practical engineering.关键词
数值计算/Cap-cyclide坐标/Wangerin函数/第一类完全椭圆积分/Jacobi椭圆函数Key words
numerical calculation/Cap-cyclide coordinates/Wangerin function/complete elliptic integral of the first kind/Jacobi elliptic functions分类
数理科学引用本文复制引用
黄华,恰汗·合孜尔,宋艳萍,努尔古丽·艾力..在Cap—cyclide坐标中Wangerin函数Nm^n（v）的高精度数值计算[J].计算力学学报,2012,29(1):38-42,5.
