Solving Ordinary Differential Equations I
PrefacetotheSecondEdition The preparation of the second edition has presented a welcome opp- tunity to improve the ?rst edition by rewriting many sections and by eliminating errors and misprints. In particular we have included new material on – Hamiltonian systems (I.14) and symplectic Runge-Kutta methods (II.16); – dense output for Runge-Kutta (II.6) and extrapolation methods (II.9); – a new Dormand & Prince method of order 8 with dense output (II.5); – parallel Runge-Kutta methods (II.11); – numerical tests for ?rst- and second order systems (II.10 and III.7). Our sincere thanks go to many persons who have helped us with our work: – all readers who kindly drew our attention to several errors and m- prints in the ?rst edition; – those who read preliminary versions of the new parts of this e- tion for their invaluable suggestions: D.J. Higham, L. Jay, P. Kaps, Chr. Lubich, B. Moesli, A. Ostermann, D. Pfenniger, P.J. Prince, and J.M. Sanz-Serna. – our colleague J. Steinig, who read the entire manuscript, for his - merous mathematical suggestions and corrections of English (and Latin!) grammar; – our colleague J.P. Eckmann for his great skill in manipulating Apollo workstations, font tables, and the like; – the staff of the Geneva computing center and of the mathematics library for their constant help; – the planning and production group of Springer-Verlag for num- ous suggestions on presentation and style.
New edition has been rewritten, errors have been eliminated and new material has been includedThe reader will benefit from many illustrations, a historical and didactic approach, and computer programsUseful to graduate students and researchers in numerical analysis and scientific computing