The paper focuses on the numerical solution of linear impulsive delay differential equations (IDDEs) using a fixed stepsize Euler scheme.
The authors begin with a brief review of existing literature on the numerical solution of impulsive differential equations. They believe that this paper is the first one on numerical methods of IDDEs. They justify their decision to use a fixed stepsize scheme and acknowledge insight gained from work with impulsive logistic equations by H. Akca, E. A. Al-Zahrani and V. Covachev [Electron. J. Differ. Equ. 2005, Conf. 12, 1–8, electronic only (2005; Zbl 1084.39002)].
In section 2 they introduce their new Euler scheme for IDDEs, which involves taking partition nodes and using a fixed stepsize. They prove their scheme to have convergence order 1 in section 3 and present an illustrative example in section 4 to demonstrate convergence to the exact solution.