A Novel Method for Nonlinear Impulsive Differential Equations in Broken Reproducing Kernel Space

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.