Abstract: In the paper, we use a modified block-by-block method to establish a high order numerical scheme for the impulsive differential equation. The modified block-by-block method is an improvement of classical block-by-block method. It is the high order numerical method for solving integral equation, and it has the advantages of the decoupled solution form at every block except the first block. Firstly, we transform the impulsive differential equation into the impulsive integral equation. Based on the impulsive integral equation form of impulsive differential equation, we establish its high order numerical scheme via modified block-by-block method. The high order numerical scheme is a decoupled solution form at each block in two adjacent impulsive points except the first block. Secondly, using the discrete Grownwall inequality, we prove that the convergence order of the numerical solution is 4. Finally, we present a series of numerical examples to support the theoretical results.

Key words: impulsive differential equation, block-by-block method, high order numerical scheme, convergence analysis