Wavelets approach to time-varying functional differential equations

Abstract

The analysis of time-varying functional differential equations via wavelets is proposed in this paper. At first, based upon some useful properties of wavelets, a special product matrix and a related coefficient matrix are applied to deal with the time-varying part. Then the wavelet stretch matrix is introduced to deal with the functional part. The unknown wavelet coefficient matrix will be found in the generalized Lyapunov equation. The local property of wavelets is completely applied to shorten the calculation process in the task.

Keywords:

• functional differential equations
• wavelets
• wavelet stretch matrix

2000 AMS Subject Classification :

• 41A35

Acknowledgements

This research was supported in part by the National Science Council of Taiwan under Grant NSC 94-2115-M-154-001.