摘要：The numerical techniques are regarded as the backbone of modern research. In literature, the exact solution of time
delay differential models are hardly achievable or impossible. Therefore, numerical techniques are the only way to find
their solution. In this article, a novel numerical technique known as Legendre spectral collocation method is used for the
approximate solution of time delay differential system. Legendre spectral collocation method and their properties
are applied to determined the general procedure for solving time delay differential system with detail error and con-
vergence analysis. The method first convert the proposed system to a system of ordinary differential equations and then
apply the Legendre polynomials to solve the resultant system efficiently. Finally, some numerical test problems are given
to confirm the efficiency of the method and were compared with other available numerical schemes in the literature.
关键词：LSCM; time delay differential equations; Legendre-Gauss-Lobatto nodes; error and convergence analysis
