Simplified reproducing kernel method for impulsive delay differential equations

In this paper, a new algorithm is presented to solve the impulsive delay initial value problems. This is the first time to propose the simplified reproducing kernel method (SRKM for short) to solve the impulsive delay differential equations. Then the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is avoided. The proposed method is proved to be stable and is not less than second order convergence. The algorithm is employed successfully in some numerical examples.