Analytic and numerical stability of functional differential equations with distributed delay

Chengjian Zhang, Stefan Vandewalle

Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium

chengjian.zhang@cs.kuleuven.ac.be

Poster

In this paper, we first study the analytic stability of the following IVPs of $N$-dimensional functional differential equations with distributed delay

$$\left \{ \begin{array}{rll} y^{'}(t)&=f(t,y(t),G(t,y(t-\tau)... ... y(t)&=\varphi(t),&t\in [t_{0}-\tau,t_0]. \end{array}\right.$$

Then, for the above IVPs, we construct a class of numerical methods, which based on the BDF methods and a linear compound quadrature formula, and obtained nonlinear and linear stability conditions of the presented methods.