ISSN:
0945-3245
Keywords:
AMS(MOS): 65L05
;
CR: 5.17
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Recently there has been considerable interest in the approximate numerical integration of the special initial value problemy″=f(x, y) for cases where it is known in advance that the required solution is periodic. The well known class of Störmer-Cowell methods with stepnumber greater than 2 exhibit orbital instability and so are often unsuitable for the integration of such problems. An appropriate stability requirement for the numerical integration of periodic problems is that ofP-stability. However Lambert and Watson have shown that aP-stable linear multistep method cannot have an order of accuracy greater than 2. In the present paper a class of 2-step methods of Runge-Kutta type is discussed for the numerical solution of periodic initial value problems.P-stable formulae with orders up to 6 are derived and these are shown to compare favourably with existing methods.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01400315
