This book deals with numerical methods for boundary-value problems in ordinary and partial differential equations (mainly linear ones) whose solutions have boundary layers due to a small positive perturbation parameter multiplying the highest derivatives. The proposed methods are robust in the sense that they effecively resolve boundary layers and preserve uniformity in the perturbation parameter both in terms of accuracy and time/memory requirements. A novice will probably find the book more useful and interesting than a specialist, as the book represents a good introduction to the field. A specialist mathematician may be disappointed by the lack of detailed proofs for most of the more complicated PDE problems. Some of those proofs exist in the not easily accessable works of one of the co-authors (Shishkin), but still remain unknown to wider public. On the other hand, detailed proofs are given for linear ODE problems everything is known about. An engineer will certainly appreciate that the book describes all possible difficulties that may be encountered when solving these complicated problems numerically. (S)he will find the robustness of the methods attractive but will be disappointed by their low accuracy (the order of accuracy is most often less than one). It is very likely that engineers will continue using the existing higher order methods, even though the requirements of those methods may be nonuniform in the perturbation parameter.

Buy this book if you have deep pockets and will indeed open your own bank. But again, if you have that kind of money, chances are that you are already familiar with the nuts-n-bolts of the banking industry, in which case the book will not be of much use. In my opinion this book would be most useful for the banking industry analysts...