The EM Method Of Stochastic Delay Differential Equations And Its Application In Hot Ice Phenomenon

This article mainly introduces the EM numerical method and its simulation of the stochastic delay differential equations. In addition the author abstract the mathematical model based on "hot ice" phenomenon in the chemical, the EM solution of the model was constructed, and the crystallization process are simulated through MATLAB simulation.Firstly, we introduce the research significance and current situation of stochastic delay differential equations in the introduction, this part expounds the current production and living and the rapid development of science and technology, the research in the field of demand are pushing us to attach the importance to the interference of random factors;The second part introduces the Brownian motion process and the Ito stochastic integral,the application form of stochastic differential equations,the Ito stochastic differential equations and the stochastic delay differential equations in this paper is given, and the concept of the stochastic delay differential equations is introduced through the population growth model;The third part summarizes the EM method of stochastic differential equations, and the convergence and stability are analyzed, extraordinaryly, we get some assignments of the parameters to simple linear stochastic differential equation and use MATLAB to make its simulation diagram, introduccing the convergence and the stability of EM method of stochastic delay differential equations,linear stochastic delay differential equations of mean square exponential stability conditions and its simulations;The fourth part mainly abstract a linear stochastic delay differential equation from the chemical reflect "hot ice", and the author gives its numerical solution, the Simulation diagram of the crystallization process are given with the help of MATLAB The fifth part is some summary and outlook for the future, live and learn, we need to explore new knowledge continuously on the basis of the existing knowledge experience;The sixth part is the main reference literature of this paper; The seventh part gives somebasic information and the educational background of the author; The eighth part is the acknowledgements.