Digitale Medien
Springer
BIT
27 (1987), S. 599-614
ISSN:
1572-9125
Schlagwort(e):
MAS
;
65L05
;
Second order initial value problems
;
oscillation problems
;
efficientP-stable methods
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract In this paper, a family of fourth orderP-stable methods for solving second order initial value problems is considered. When applied to a nonlinear differential system, all the methods in the family give rise to a nonlinear system which may be solved using a modified Newton method. The classical methods of this type involve at least three (new) function evaluations per iteration (that is, they are 3-stage methods) and most involve using complex arithmetic in factorising their iteration matrix. We derive methods which require only two (new) function evaluations per iteration and for which the iteration matrix is a true real perfect square. This implies that real arithmetic will be used and that at most one real matrix must be factorised at each step. Also we consider various computational aspects such as local error estimation and a strategy for changing the step size.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01937279
Permalink
| Bibliothek |
Standort |
Signatur |
Band/Heft/Jahr |
Verfügbarkeit |
