more recently there has been increasing emphasis on just a few classes of methods for which sophisticated implementations now exist. This book places much more emphasis on such implementations- and on the important topic of stiffness- than did its predecessor. Also included are accounts of the structure of variable-step, variable-order methods, the Butcher and the Albrecht theories for Runge- Kutta methods, order stars and nonlinear stability theory. The author has taken a middle road between analytical rigour and a purely computational approach, key results being stated as theorems but proofs being provided only where they aid the reader' s understanding of the result. Numerous exercises, from the straightforward to the demanding, are included in the text. This book will appeal to advanced students and teachers o numerical analysis and to users of numerical methods who wish to understand how algorithms for ordinary differential systems work and, on occasion, fail to work.