Authored by one of the world´s leading authorities on numerical methods this update of one of the standard references on numerical analysis, outlines recent developments in the field and presenting a detailed overview of the area. The only book to provide both a detailed treatment of Runge-Kutta methods and a thorough exposition of general linear methods, it also provides practical guidance on solving equations associated with general linear methods, thus providing assistance to those who wish to develop their own computer code. Accompanied by a website hosting solutions to problems and slides for use in teaching Illustrated throughout by worked examples of key algorithms. Presents practical guidance on solving equations associated with general linear methods Gives an introductory overview of the field before going on to describe recent developments. All methods are illustrated with detailed examples and problems sets.