Types Of Delay Differential Equations Imex¦È-method Stability

Delay differential equations(DDEs) is an important branch of functional differential equations. It plays an important role in automatic control, biology, medical science, aviation, economics and so on, so the numerical analysis for DDEs is also very important. Many papers have focused on this topic, and the research in this field has made great progress in recent forty years. But up to now there have been few results of additive methods for DDEs. In this paper, we discuss the asymptotic stability of IMEXθ-method for delay differential equation with several delay terms, pantograph equation and pantograph equation of neutral type, the main results are as follows:In chapter 2, we analyze the asymptotic stability of IMEXθ-method for delay differential equation with several delay terms, and obtain the sufficient and necessary conditions for the numerical solution to preserve the asymptotic stability.In chapter 3, we investigate the asymptotic stability of IMEXθ-method for pantograph equation, and gain the sufficient conditions for the numerical solution to preserve the asymptotic stability.In chapter 4, we deal with the asymptotic stability of IMEXθ-method for multi-pantograph equation. The sufficient conditions for the numerical solution to preserve the asymptotic stability are obtained.In chapter 5, we study the asymptotic stability of IMEXθ-method for pantograph equation of neutral type, and get the sufficient conditions for the numerical solution to preserve the asymptotic stability.Numerical experiments at the end of each chapter confirm the theoretical analysis.