第一类弱奇异Fredholm积分方程的配置解法

A Collocation Method for the First Kind of Weakly Singular Fredholm Integral Equations

对于具有弱奇异性的第一类Fredholm积分方程提出了配置法,该方法的关键思想在于将积分算子的弱奇异核分裂成有限项,使得弱奇异性能够用分部积分加以克服.理论分析和实验显示,该方法的精度可以达到O(hm+1),这里h为步长,m为所用基函数的最高次.

A collocation method is introduced for a class of Fredholm integral equation of its first kind with weakly singular kernels. The key idea of this method is splitting the weakly singular kernel of the integral operator into finite parts so that the weak singularity is concentrated on one which can be analytically solved using integration by parts. Theoretical analysis and numerical examples show this method can achieve accuracy O（h^m＋1 ）, with h being the step size, and the highest order of the basis function.