An explicit Maclaurin series solution to a classic non-autonomous abstract evolution equation
- Resource Type
- Working Paper
- Authors
- Bassom, Andrew; Howlett, Phil; Taylor, Peter
- Source
- Applied Mathematics Letters, 139, May 2023, 108537
- Subject
- Mathematics - Dynamical Systems
34A25, 34A30, 34G10
- Language
It is well known that the non-autonomous scalar differential equation of evolution has a unique solution given by an elementary exponential function. In general there is no such analogous solution to the corresponding non-autonomous evolution equation for square matrices. In this paper we propose and justify an explicit Maclaurin series solution to a classic non-autonomous abstract evolution equation for bounded linear operators on Banach space.
Comment: 30 pages. No figures. Corrected version of article published in Applied Mathematics letters