文档介绍：???????? ???????? ???????????????????????????????????????????????????????????????????????2008?5??????????????? Classi?ed Index: .: Dissertation for the Master Degree in Science NUMERICAL METHODS ANALYSIS FOR SOME KINDS OF DELAY DIFFERENTIAL EQUATIONS Candidate: Sui Zhenan Supervisor: Prof. Zhao Jingjun Academic Degree Applied for: Master of Science Specialty: Computational Mathematics Af?liation: Department of Mathematics Date of Defence: May, 2008 Degree-Conferring-Institution: Harbin Institute of Technology ?????????????????Ч???????????????????????????????????????????????????????????????????Runge-Kutta????????θ-???????????????????????????????????????????????Ч?????ν???: ????????Runge-Kutta??????????????Runge- Kutta????????????????????????????????????????????????????Runge-Kutta??????????????????????????????????Runge-Kutta??????????????????????????????????????????????????????????????????????????????????????????????????????????τ(0)-???????????Gauss???LobattoIIIA???LobattoIIIB???τ(0)-????????????????θ-???????????????????????????????????????????????????????????????????????????????????????????????????????????– I –??????????????? Abstract This prises three independent parts, which involves semi-linear parabolic problems, delay semi-linear parabolic problems, two order delay differen- tial equations and mixed equations. The numerical methods applied to these problems include exponential Runge-Kutta methods, symmetric methods andθ-methods. The issue involves convergence, delay-independent stability, delay-dependent stability, os- cillation and natural continuous extension. The thesis anized as follows: The ?rst part deals with exponential Runge-Kutta methods. In Chapter 2, we discuss the convergence and natural continuous extension of exponential Runge-Kutta methods for semi-linear parabolic problems, and analyze the convergence of the nat- ural continuous extension and its derivatives. The main result is: the convergence orders of exponential