在再生核空间中求解非线性奇异两点边值问题

Solving Nonlinear Singular Two-point Boundary-value Problem in the Reproducing Kernel Space

该文建立了一个迭代方法求解一类奇异两点边值问题（x^αu′）′=f（x,u,u′）,其中x∈（0,1）,α＆lt;2.解的表达式是在再生核空间W2[0,1]中以级数的形式给出的.近似解一致收敛到准确解.并且,误差是单调下降的.最后通过一些数值算例论述了所提方法的正确性与有效性.

In this paper,the authors establish an iterative method to compute solution for a class of singular two-point boundary value problems（x~αu′）′= f（x,u,u′）,where x∈（0,1）,and＆lt;2.Representation of the solution is given in the form of series in the reproducing kernel space W_2[0,1].The n-term approximation u_n（x） is proved to converge to the exact solution. Furthermore,the approximate error of u_n（x） is monotone decreasing.Some numerical examples are illustrated to demonstrate the accuracy of the present method.