Structure and stabiliy of finite dimensional approximations for functional differential equations. (English) Zbl 0578.34051
Summary: This paper deals with the structural and stability properties of the averaging approximation scheme for linear retarded functional differential equations. Both in the discrete- and in the continuous-time case the structure of the approximating systems is shown to be analogous to the structure of the underlying retarded equation. Moreover, it is shown that the approximating systems are exponentially stable in a uniform sense if the original system is asymptotically stable.
MSC:
34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
65L07 | Numerical investigation of stability of solutions to ordinary differential equations |