Solving ordinary differential equations. Springer series in computational mathematics; Bd. 14.

The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). There is a chapter on onestep and extrapolation methods for stiff problems, another one on multistep methods and general linear methods for stiff problems, and a third one on the treatment of singular perturbation problems and differential-algebraic systems. The beginning of each chapter is of an introductory nature, followed by practical applications, the discusssion of numerical results, theoretical investigations on the order of accuracy, linear and non-linear stability convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (eg, in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programmes are presented. This monograph on applied mathematics, numerical analysis and scientific computation is intended for researchers, teachers and students.