In this article, a new algorithm is presented to solve the nonlinear impulsive dif- ferential equations. In the first time, this article combines the reproducing kernel method with the least squares method to solve the second-order nonlinear impulsive differential equations. Then, the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is avoided. The algorithm is employed successfully on some numerical examples.

中文翻译：

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破碎再生核空间非线性脉冲微分方程的一种新方法

在本文中，提出了一种求解非线性脉冲微分方程的新算法。本文首次将再生核法与最小二乘法相结合求解二阶非线性脉冲微分方程。然后，证明了数值解的一致收敛性，避免了耗时的施密特正交化过程。该算法在一些数值例子中得到了成功应用。