A high speed and high accuracy simulator whose data-handling is light and whose weak stability is assured even for stiff systems is discussed. This work is a part of CAD package : CADPACS-T which has been under development for the purpose of designing control systems utilizing TSS of a large scale digital computer in our laboratory. This simulator realizes high accuracy, high computational speed and high reliability adopting A-stable extrapolation methods to transform into a difference system, a recursive formula of an output interval to solve the difference equation, automatic choice of an optimal step length such that minimizes an predicted error, and evaluating error bounds closely near the actual errors in the point of numerical calculation. Moreover, in the point of data management, this realizes separation of program modules from data, common utilization of data and separation of investigation from simulation.