中文摘要：

本文研究时滞积分微分方程的数值方法．通过改造现有常及离散型延迟微分方程的数值方法，并匹配以适当数值求积公式，构造了求解时滞积分微分方程的Rosenbrock方法，导出了其稳定性准则．数值例子阐明了所获方法的计算有效性．

英文摘要：

The numerical methods are studied for a class of delay integro-differential equations. By adapting the existed numerical methods for ordinary and delay differential equations, and matching certain suitable numerical quadrature formulas, Rosenbrock methods are constructed for delay integro-differential equations,the stability criteria of the methods are derived. The numerical examples illustrate the computational effectiveness of the obtained methods.