In this letter, to fit the character of solutions to impulsive boundary value problems (IBVPs), we firstly construct a piecewise continuous space using the reproducing kernel function (RKF) of smooth reproducing kernel Hilbert space (RKHS) $W^3$. Then we present a fourth order convergent collocation approach for IBVPs by using the piecewise continuous basis functions yielded by RKFs in $W^3$. Also, the convergence order of our approach is proved. The accuracy and convergence order are shown numerically.

中文翻译：

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一种求解脉冲边值问题的核函数算法

在这封信中，为了适应脉冲边值问题（IBVPs）解的特点，我们首先使用平滑再生核希尔伯特空间（RKHS）的再生核函数（RKF）构造一个分段连续空间。$W^3$. 然后，我们通过使用 RKF 产生的分段连续基函数，提出了 IBVP 的四阶收敛配置方法$W^3$. 此外，证明了我们方法的收敛顺序。精度和收敛顺序以数字形式显示。