Stability Analysis Of Second Order Delay Differential Equations

Second-order delay differential equations often arised in biology, impulse and control theory and so on. The stability study can provide theoretical support for engineering and technology field, which have been widely studied by many authors. However, because of the constraint of delay conditions, there are few works about theoretical stability and numerical stability for second-order multi-delay differential equations. Therefore, it is necessary to investigate stability of the numerical methods for second-order multi-delay differential equations.In this paper, it mainly discuss a class of second-order multi-delay differential equations, concerning with theoretical stability and numerical stability of solutions. Firstly, based on the root distribution theorem of exponential polynomials,sufficient condition of theoretical stability is given for second-order multi-delay differential equations. Secondly, it discussed the numeri-cal stability of θ-method applied to this second-order multi-delay differential equations, and it is obtained that θ-method is asymptotic stable when satisfied certain conditions. At last, this paper analyzes the numerical stability of Runge-Kutta(RK) method solving second-order multi-delay differential equations. It is obtained that Runge-Kutta(RK) method is asymptotic stable when satisfied some conditions.