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| The high precision numerical calculation of Wangerin function Nmn(ν) based on Cap-cyclide coordinates |
| Received:June 08, 2010 Revised:December 15, 2010 |
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| DOI：10.7511/jslx20121007 |
| KeyWord:numerical calculation Cap-cyclide coordinates Wangerin function complete elliptic integral of the first kind Jacobi elliptic functions |
| Author | Institution |
| 黄华 |
新疆农业大学 数理学院, 乌鲁木齐 |
| 恰汗·合孜尔 |
新疆农业大学 数理学院, 乌鲁木齐 |
| 宋艳萍 |
新疆农业大学 数理学院, 乌鲁木齐 |
| 努尔古丽·艾力 |
新疆农业大学 数理学院, 乌鲁木齐 |
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| Abstract: |
| In Cap-cyclide coordinates, the Wangerin function Nmn(ν), 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 Nmn(ν), 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 Jacobi 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 Nmn(ν) upon these two steps. The result provides the theoretical basis for further research on convergence and stability of Wangerin function Nmn(ν), and shows that it is very useful to practical engineering. |
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