Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems by Ernst Hairer
The subject of this book is the solution of stiff differential equations and of differential-algebraic systems. This second edition contains new material including new numerical tests, recent progress in numerical differential-algebraic equations, and improved FORTRAN codes.
From the reviews:
A superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text. --MATHEMATICS TODAY