On Asymptotic Approximations to a Class of Regular Perturbation Problems

Abstract

A new approach to a class of regular perturbation problems of common occurrence in lubrication theory is presented. The approach is not dependent on extensive algebraic manipulation and predicts results which, apart from numerical rounding error, are in exact agreement with standard theory. Three illustrative examples are studied in detail and it is demonstrated that asymptotic approximations obtained through use of the approach can be of a substantially higher order than approximations at present in the literature.