刚性延迟系统仿真算法及其理论

This project deals with the simulation algorithms and their theory of stiff delay systems, investigates linear and nonlinear stability of the systems and their algorithms, and presents new D-convergence criteria of the variable-coefficient linear multistep methods, Runge-Kutta methods and general linear multistep methods for the above systems. Based on both the sufficient theoretical research and a lot of numerical tests, we construct parallel two-process multistep Runge-Kutta methods, Adams methods, BD methods and diagonal iteration Runge-Kutta methods for delay systems. With these, a simulation algorithm software for the delay systems are formed. This project completes thirty papers, in which eight papers have been embodied in SCI, ten papers published in the home-key periodicals and one paper accepted by a SCI journal. In view of these, this project has fully completed the desired plan. The obtained results enhance the simulation algorithms theory for stiff delay systems and provide some new simulation tools for the engineering areas such as biology, automatic control and so on. Hence, it is sure that these results will have the wide applications in practice.

探索求解刚性延迟问题的仿真数值算法的误差与稳定性特征，获取其算法理论，并在本理论的指导及充分仿真实验的基础上筛选出高效仿真算法，使其形成具一体化、人一机交互功能及专家功能的刚性延迟问题仿真算法软件包。本课题的研究，在理论上将丰富系统仿真算法的内涵，在实践上将在生物学、自动控制及诸工程领域有广泛应用前景。