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Analytical and Numerical Stability for Several Classes of Delay Differential Equations

Author: LiChaoQun
Tutor: HuangChengMing
School: Huazhong University of Science and Technology
Course: Computational Mathematics
Keywords: Delay Differential Equations Rational approximation A- acceptability General linear methods Abstract Cauchy Problem Characteristic root calculation
CLC: O241.8
Type: Master's thesis
Year: 2005
Downloads: 262
Quote: 1
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Abstract


There is a lot of time in the science and engineering fields of ecology, economics , physics , chemistry , and automatic control delay system, delay system characteristics is that the evolution of the system is dependent on the information of the past . Build this system for the mathematical model is the delay differential equations ( Delay Differential Equations , hereinafter abbreviated as DDEs in ) , that is, the differential equation contains one or more delay . In general , the common delay differential equations , only a handful have access to the analytical expression of the theoretical solution , such differential equations numerical processing is very necessary . So far, the stability of the system theory of delay differential equations , delay differential equations , estimated the value of the delayed items and so made ??a lot of achievements . In this thesis, delay differential equations in the theory and numerical solutions of stability analysis . Chapter II deals with the exponential function exp ( z ) rational approximation , the problem is closely related to the Study on the stability of the numerical method . A class of two-parameter exponential function exp ( z ) arbitrary high order rational approximation , access to the A- acceptability and L- acceptability of necessary and sufficient conditions . The third chapter discusses the stability of neutral delay differential equations . First, we get a class of nonlinear neutral equations ( k , p , 0 ) - algebraically stable general linear methods for the numerical stability of the results , in particular , is to prove unconditional remain in the constraint grid circumstances algebra stability of general linear methods stability of the analytical solutions . Followed by further discussion of the stability of the analytical solution of implicit nonlinear neutral delay equation . The fourth chapter of linear delay differential equations to determine the stability . Characteristic roots for delay differential equations constitute a delay differential equation solvers semigroup infinitesimal generator of the spectrum , we use the theta - method for discrete delay differential equation solvers semigroup infinitesimal generator to obtain the characteristic roots of delay differential equations numerical approximation , the characteristic root position determination system stability delay differential equations . On the other hand , the numerical solution of delay differential equations into solving the discrete abstract Cauchy problem . Theta - method numerical experiments in this paper .

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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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