Some numerical methods of determining the behavior of systems of differential equations in relation to the initial conditions (Q1080622)

The author considers the linear system \(\dot x=A(t)x\) where x(t) is an abstract function and A(t) an abstract operator-function, compact in a Banach space. Particular attention is paid to the case of A piecewise constant, and the appropriate form of the fundamental operator and of the resolvent is indicated. The paper refers extensively to other papers and there is no analysis leading up to the stated results. The treatment is highly abstract and it is not immediately obvious how the paper will be useful in treating actual numerical problems.