Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems

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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