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首页> 外文会议>International Conference on Information and Computing Science;ICIC '09 >Approximate Solutions of a Hypersingular Boundary Integral Equation
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Approximate Solutions of a Hypersingular Boundary Integral Equation

机译：超奇异边界积分方程的近似解

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In the paper, a reproducing kernel method of solving hypersingular integral equations (HSIE) with cosecant kernel is proposed. Difficulties lie in its singular term of solving HSIE. In order to remove singular term, hypersingular term with square cosecant kernel is transformed into singular term with Hilbert kernel. Subsequently, by making a equivalent transformation singular term with Hilbert kernel is removed. It's advantages the series representation of solution is obtained in a reproducing kernel Hilbert space. On the other hand, the representation of reproducing kernel becomes simple by improving the definition of traditional inner product and requirements for image space of operators are weakened comparing with traditional reproducing kernel method. The final numerical experiments illustrate the method is efficient.
机译：提出了一种用余割核求解超奇异积分方程（HSIE）的再生核方法。困难在于解决HSIE的单一术语。为了去除奇异项，将具有平方余割核的超奇异项转换为具有希尔伯特核的奇异项。随后，通过对Hilbert核进行等效变换，去除了奇异项。在可再生内核Hilbert空间中获得解决方案的序列表示是有利的。另一方面，通过改进传统内部积的定义，再现核的表示变得简单，并且与传统再现核方法相比，运算符对图像空间的要求被削弱。最终的数值实验表明该方法是有效的。

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