• 论文 •

### Legendre小波求解超奇异积分

1. 燕山大学理学院, 河北秦皇岛 066004
• 收稿日期:2011-11-16 出版日期:2012-05-15 发布日期:2012-05-20
• 基金资助:

河北省自然科学基金(E2009000365)资助项目.

Chen Yiming, Yi Mingxu, Wei Jinxia, Chen Juan. LEGENDRE WAVELET FOR SOLVING SUPERSINGULAR INTEGRAL[J]. Mathematica Numerica Sinica, 2012, 34(2): 195-202.

### LEGENDRE WAVELET FOR SOLVING SUPERSINGULAR INTEGRAL

Chen Yiming, Yi Mingxu, Wei Jinxia, Chen Juan

1. College of Sciences, Yanshan University, Qinhuangdao 066004, Hebei, China
• Received:2011-11-16 Online:2012-05-15 Published:2012-05-20

The numerical methods of supersingular integral are always an important topic in recent years. Based on the definition of Hadamard finite-part integral of the supersingular integral, we have given a method which calculates the supersingular integral by using Legendre wavelet in this paper. When the singular point is located in the interval, as Legendre wavelet has a better orthogonality, good explicit expression and computability of the wavelet function, we can convert the singular point of interval into the endpoint of interval, and then by making use of the definition of Hadamard finite-part integral where the singular point is located at the endpoint of interval, we can compute the p+1(pN+) order supersingular integral. Finally, the feasibility and validity of the method can be proved by the examples shown in the work.

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