Convergence of block boundary value methods for solving delay differential algebraic equations with index-1 and index-2

In this paper, we propose block boundary value methods to solve the initial value problem of delay differential algebraic equations. For the problems with index-1 and index-2, we give the error estimate of the proposed methods respectively. It is shown that, under certain conditions, the convergence order of the proposed methods is consistent with the underlying one in the case of ordinary differential equations. Finally, some numerical experiments are carried out to demonstrate the effectiveness of the theoretical results.