Two Families Of Linearized Methods For Delay Differential Equations

Delay differential equations(DDEs) provide a class of powerful models for many phenomena in applied sciences,such as physics,biology,medicine,engineering,auto-control, aerospace,economics and so on.Since their theoretical solutions could be obtained only in very restricted cases,we have to use numerical methods for solving DDEs.In the last decades,theory of computational methods for DDEs has been studied by many authors and a significant number of important results have been found.This thesis includes four chapters.In the presented chapters,we study linearizedΘ-methods and piecewise-linearized methods for delay differential equations.Firstly,we summarize the application and classification of delay differential equations and review the status and development of numerical methods for solving delay differential equations.The difficulties in solving delay differential equations are shown and hence the research topics of this paper are proposed.In chapter two and three,we develop the linearizedΘ-methods and piecewise-linearized methods for solving delay differential equations.Two families of methods' development in the area of differential equations are reviewed.The linearizedΘ-methods and piecewiselinearized methods for solving delay differential equations are introduced.The stability and error of the methods are discussed.The conclusions are proven by numerical experiments.Finally,the work of the paper are summarized and the prospect of the research are given.