The Research Of Convergence And Stability In The Stochastic Delay Differential Algebraic System Of θ Method

Differential algebraic system has been widely used in many fields such as opti-mization and control, power and circuit analysis, computer-aided design, biology, the national economy and so on. However, these areas often exist uncertainties interfer-ence. Therefore, we can more realistic reflect and simulate the real problem by using the stochastic delay differential algebraic system.As we known, the stochastic delay differential algebraic systems contain random items, uncertainties and algebraic constraints, most of the stochastic delay differential algebraic systems are unable to obtain the theoretical solution. Therefore, the study of the numerical methods becomes more urgent and important. The convergence and stability of numerical studies is an essential part in the process. More and more scholars are concerned about convergence and stability of numerical solution.The main work is as follows:The first chapter, we review the research background and current research status.The second chapter, equation and its related concepts are given in the stochastic delay differential algebraic system and it is proved that the θ method is 1/2 order of convergence.The third chapter, the stability of the numerical method is discussed and it is proved that the method is mean square stable under suitable conditions.The fourth chapter, the conclusion of the second and third chapter are verified through numerical experiments.