对偶边界元法中对数奇异积分的计算

采用三次多项式坐标变换计算边界元积分的方法 ,对对偶边界元法中含对数奇异积分的计算进行研究。几个解析积分算例和运用对偶边界元法对二维平面裂纹问题裂尖应力强度因子的计算结果表明 。

基于小波基函数的奇异积分求积算法

该文针对一类基于小波基函数的对数奇异积分提出了乘积积分方法.该方法可以通过对小波基函数作适当的数值处理,然后应用基本积分公式快速实现.相对于传统的数值积分方法,该方法能够快速有效地计算出奇异积分的准确解.最后,给出了几个数值算例,证明了该方法的有效性.

Integral Representation of the Manifold Solution for New Class of the Volterra Type Integral Equation with a Boundary Singularity in the Case, When Kernel Contain Logarithmic Singularity and its Power

In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity and function with singular point. The problem investigation this type integral equation at n = 2m reduce to problem investigate the Volterra type integral equation （1） for n = 2 the theory for which was constructed in [2]. In this work, we investigation integral equation （1） at = 2m ＋ 1 In this case, we investigate integral equation （1） reduction it＇s to m integral equation type [2] φ（x）＋∫xa[p1＋p2 ln（x-a/t-a）]φ（t）/t-a dt=f（x）and one the following integral equation [1] ω（x）＋p3∫xω（t）/ a t-adt=g（x）.