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Delay differential equations stability

Author: LiuYang
Tutor: LvWanJin
School: Heilongjiang University
Course: Applied Mathematics
Keywords: Delay differential equations Linear Multistep Improved linear multistep Asymptotic stability Schur polynomial
CLC: O241.8
Type: Master's thesis
Year: 2011
Downloads: 7
Quote: 0
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Abstract


Delay differential equation as an important branch of functional differential equations , is widely used in many fields of the physical , biological , economic , medical , engineering , and aerospace . Therefore , its numerical algorithm has important scientific significance . The numerical stability of the existing literature on the delay differential equations have done a series of studies , but also made ??some progress . However , most of the numerical method is only limited to the low-level approach , at home and abroad there are few studies of higher - order method . This article mainly through improved linear multistep method of single delay differential equations and multi- delay differential equations numerical stability . In the first chapter , we briefly delay differential equations in different fields of application , as well as at home and abroad in recent decades on single delay differential equations and multi numerical stability of delay differential equations . And , on this basis , the main work of this paper . In the second chapter of this paper , we introduce a single delay differential equations and the concept of multi- delay differential equations , and analytical solutions of the two equations asymptotically stable , and briefly describes the basic definitions and A stable linear multistep definition , research linear multistep methods for numerical stability , necessary and sufficient conditions of asymptotically stable . Last elaborated Chapter Summary . In Chapter III of this paper , we introduce the numerical methods used in this paper processing delay differential equations , linear multistep that improvement . Integer nodes on a single numerical stability of delay differential equations and the necessary and sufficient condition for the method is asymptotically stable . Finally , through concrete examples to prove it . Node integer delay differential equations in Chapter IV of this paper , we study the numerical stability and the necessary and sufficient condition for the method is asymptotically stable . Finally , through concrete examples to prove it . In the fifth chapter of this article , based on research on these issues is the summary of the summary .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations
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