求一类四阶奇异边值问题的数值解

Numerical Solution for Solving a class of Singular Fourth-order Boundary Value Problem

在再生核空间W5[0,1]中给出了求解一类四阶奇异方程的算法,给出了精确解的级数形式的精确表达,证明了近似解及其各阶导数一致收敛于精确解及其各阶导数.算例的数值结果验证了该方法的高效性.

In this paper,a new numerical algorithm for solving a class of singular fourth-order boundary value problems in the reproducing kernel space.The representation of the exact solution is given in the series form,and the numerical solution is proved to uniformly converge to the exact one.Numerical results demonstrated that the algorithm is of high precision.