Asymptotic series solutions of linear equations systems

In this thesis, asymptotic series solutions fort he systems of the form; X^'=A(z)X are optained. Three different choices for A(z) are considered. The first one is; A(z)=∑_(k=0)^∞▒A_k (z) z^(-k), which includes powers of z. The second one is more general form; A(z)=∑_(k=0)^∞▒A_k (z) z^(-k+r), and finally the matrix A depends on both independent variable z and a parameter μ that is A(z,μ)=∑_(k=0)^∞▒A_k (z) μ^(-k+1), Since the resultant series yield information about the solution for large values of the independent variable, the convergence of the solutions are also analyzed.