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A new method for solving hypersingular integral equations of the first kind

โœ Scribed by Zhong Chen; YongFang Zhou

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
264 KB
Volume
24
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

A simple and efficient method for solving hypersingular integral equations of the first kind in reproducing kernel spaces is developed. In order to eliminate the singularity of the equation, a transform is used. By improving the traditional reproducing kernel method, which requires the image space of the operator to be W 1 2 and the operator to be bounded, the exact solutions and the approximate solutions of hypersingular integral equations of the first kind are obtained. The advantage of this numerical method lies in the fact that, on one hand, the approximate solution is continuous, and on the other hand, the approximate solution converges uniformly and rapidly to the exact solution. The validity of the method is illustrated with two examples.

๐Ÿ“œ SIMILAR VOLUMES

An initial value method for solving Fred
An initial value method for solving Fredholm integral equation of the first kind
โœ V. Vemuri; Fang-Pai Chen ๐Ÿ“‚ Article ๐Ÿ“… 1974 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 817 KB

T?w d@culties in solving Fredholm integral equations of the first kind are well bnown. A classical method has been to convert the equation into a set of m linear algebraic equation8 in n unknown8 (rng n). For computational convenience, it is customary to force m = n and solve the resulting ill-condi