基于再生核的样条插值求解积分方程

Solving Integral Equation by Using Spline Interpolation Based on Reproducing Kernel

研究第二类积分方程的算法。首先由再生核函数的特殊性简洁地构造一次样条函数空间的一组基底;接着在这个基底下给出这类积分方程的有效算法;然后证明该算法的收敛阶为二阶;最后依照这种算法做了一些数值实验,并与文献中给出的其他算法比较,结果说明本研究算法更有效。

The algorithm of the second type of integral equation is studied in the paper. Firstly,a set of bases for the space of the primary spline function is concisely constructed based on the particularity of the reproducing kernel function. And then,an effective algorithm for this type of integral equation is given under this base. Furthermore,it is proved that the convergence order of the algorithm is not less than two-order.Finally,some numerical experiments according to this algorithm prove that the algorithm given in this paper is more effective compared with other algorithms given in the literatures.