分片光滑边值问题的再生核方法

Reproducing Kernel Method for Piecewise Smooth Boundary Value Problems

一种高效的再生核算法(RKM)被提出用于解决分片光滑边值问题(BVP).通过定义算子L:W23[0,1]→L2[0,1],应用再生核算法,解决了较为复杂的分片光滑边值问题.对定理的证明保证了算法理论的正确性,进而得到近似解un(x)以O(h2)收敛于精确解.即:在范数‖·‖W23意义下un(x)有不低于二阶的收敛性.数值算例表明算法正确、简便、有效.

In this paper,an efficient reproducing kernel method(RKM) is proposed for solving the piecewise smooth BVP.By defining an operator L:W23|0,1]→L2[0,1] and applying the reproducing kernel property,we have skillfully solved the complex piecewise smooth BVP.The theorems show the accuracy of the algorithm.Furthermore,we get that the approximate solution un(x) convergence to the exact one with order O(h2).That is,un(x) has second order convergence in the sense of norm ‖·‖W23.Finally,some numerical experiments are given to illustrate the algorithm is accuracy,simple and efficient.