Semester
Spring
Date of Graduation
2006
Document Type
Dissertation
Degree Type
PhD
College
Eberly College of Arts and Sciences
Department
Mathematics
Committee Chair
Harry Gingold
Abstract
New methods for both asymptotic integration of the linear differential systems Y'(t) = [D( t) + R(t)]Y( t) and asymptotic summation of the linear difference systems Y(t + 1) = [D(t)+ R(t)]Y(t) are derived. The fundamental solution Y(t) = phi( t)[I+P(t)] for differential and difference systems is constructed in terms of a product. The first matrix function phi(t) is decided by the diagonal matrix D(t) and the second matrix I + P(t) is a perturbation of the identity matrix I. Another fundamental solution Y( t) = [I + Q(t)]phi( t) is also constructed for difference systems. Conditions are given on the matrix [D(t) + R( t)] that allow us to represent I + P( t) or Q(t) + I as an absolutely convergent resolvent series without imposing stringent conditions on R(t). In particular the analogs, in the setting of difference equations, of fundamental theorems of Levison and Hartman-Wintner are shown to follow from one and same theorem in this work.
Recommended Citation
Xue, Fei, "Asymptotic solutions of almost diagonal differential and difference systems" (2006). Graduate Theses, Dissertations, and Problem Reports. 4280.
https://researchrepository.wvu.edu/etd/4280