Springer Series in Computational Mathematics

2 primary works

Solving Ordinary Differential Equations I

by Ernst Hairer, Syvert P Norsett, and Dr Gerhard Wanner

Published 16 April 2008

This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included.

Solving Ordinary Differential Equations II

by Ernst Hairer and Dr Gerhard Wanner

Published July 1991

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.