Stability Analysis Of A Class Of Delay Integro Differential Equations

Many phenomena in science and engineering can be modelled by initial value problems for functional differential equations. Delay integro-differential equations are one of the important member in the family of functional differential equations and have been used widely in physics, engineering, mechanics, medicine and economy, and many other areas. Since we can not obtain the accurate analytical solution of most model equations of practical problems, the research on numerical method is necessary. Many scholars and experts concerned on this research in the last decade and obtained a large number of important results. However, they main consider delay integro-differential equations with integral term (?)and the research on equations with integral term (?)is still very little.In this paper, we main study the analytical and numerical solution of the delay integro-differential equations with three real coefficients. In the first chapter, we will give a brief introduction to the application of delay differential equations in different areas and the development of the theory about the stability of the analytical and numerical solution.In chapter 2, at the beginning, through a skill handing of the equation, we will get an 2-dimensional delay differential equation, then we use boundary locus method to analyse the asymptotic stability of the analytical solution of the equation. Through analysing the properties of the characteristic equation, the delay dependent analytical asymptotic condition and asymptotic stability region will be obtained.In chapter 3, with the same method used in the previous chapter, the stability of numerical solution of the delay equation will be studied. We apply the trapezoidal method to discretize the equation, then by discussing the characteristic equation and characteristic curves, the numerical asymptotic stability region will be obtained. In the final of this chapter, by comparing the results on analytical and numerical stability which obtained in the previous two chapters, we will derive the main result of this paper.In chapter 4, we will present some numerical experiments to verify the correctness of the conclusions.Finally, we will do some summary and describe possible future research.