This book considers the practical solution of one-dimensional integral equations. Both integral equations, and methods for solving them, come in many forms and we could not try, and have not tried, to be exhaustive. For the problem classes covered, we have used the ‘classical’ Fredholm/Volterra/first kind/second kind/third kind categorisation. Not all problems fit neatly into such categories; then the methods used to solve standard classes of problems must be modified and tailored to suit the needs of nonstandard ‘real life’ problems. It is hoped that the nature of any such modifications will be obvious to the intelligent reader. Not all categories of problems seem equally important (i.e. frequent) in practice; we have tried to spend most time on the most important classes of problems.

We have also been selective in the choice of methods covered. Here, personal likes and dislikes have helped the selection process, but we have also taken particular note of the fact that the cost of solving even a one-dimensional integral equation of Fredholm type can be unexpectedly high. Methods which converge slowly but steadily are therefore not very attractive in practice and particular emphasis is placed on the ability of a given method to obtain rapid convergence, to provide computable error estimates and to produce reliable results at relatively low cost.

It is hoped that the book will serve as a reference text for the practising numerical mathematician, scientist or engineer, who finds integral problems arising in his work.