ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991):65L06
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. In recent years, much insight into the numerical solution of ordinary differential equations by one-step methods has been obtained with a backward error analysis. It allows one to explain interesting phenomena such as the almost conservation of energy, the linear error growth in Hamiltonian systems, and the existence of periodic solutions and invariant tori. In the present article, the formal backward error analysis as well as rigorous, exponentially small error estimates are extended to multistep methods. A further extension to partitioned multistep methods is outlined, and numerical illustrations of the theoretical results are presented.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050469
