The reproducing kernel functions (RKFs) and related theory have been employed to deal with the numerical solutions of boundary value problems (BVPs). The existing RKFs based approaches for BVPs have global convergence order two and three in the reproducing kernel Hilbert spaces (RKHSs) $W^3$ and $W^4$, respectively. The global convergence order of the present new method is four and six in the RKHSs $W^3$ and $W^4$, respectively. The error analysis is also discussed. To show the effectiveness, the numerical results of experiments are compared with the existing RKFs based techniques.

中文翻译：

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一种新的基于高阶精确再现核的边值问题方法

再现核函数（RKF）和相关理论已用于处理边值问题（BVP）的数值解。现有的基于RKF的BVP方法在再现内核希尔伯特空间（RKHS）中具有全局收敛阶数2和3。${\mathrm{w\; ^}}^3$ 和 ${\mathrm{w\; ^}}^4$， 分别。在RKHS中，当前新方法的全局收敛阶数为4和6${\mathrm{w\; ^}}^3$ 和 ${\mathrm{w\; ^}}^4$， 分别。还讨论了错误分析。为了证明其有效性，将实验的数值结果与现有的基于RKF的技术进行了比较。