Abstract
A variant of the Gronwall-Bellman inequality is used to develop new bounds on solutions to the fundamental singular integral equations that arise in the error analysis of the Liouville-Green (or WKB) approximation. Consequently, new improved error bounds are obtained from the Liouville-Green approximation to the solution of the differential equation d 2W dT 2 − q(T) W = 0 , where the function q is real and twice continuously differentiable and does not vanish.
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