Determination of upper and lower bounds for solutions to linear differential equations
R. M. Durstine, D.H. Shaffer · Quarterly of Applied Mathematics · 1958
Analytic upper and lower bounds may be constructed on the solutions to linear differential systems of a certain kind, as described in this paper.The principal requirement of the method presented here is that two functions satisfying the boundary conditions placed on the system-and certain other conditions-must first be constructed.The bounds are then generated as linear combinations of these two functions.The development proceeds as follows.Consider a linear differential equation