THE CHEBYSHEV METHODS OF PANOVSKY AND RICHARDSON AS RUNGE-KUTTA-NYSTROM METHODS

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:61

Article

COLEMAN, JP ; BOOTH, AS

关键词: HYBRID METHODS;    RUNGE-KUTTA-NYSTROM METHODS;    COLLOCATION;    2ND-ORDER DIFFERENTIAL EQUATIONS;    CHEBYSHEV METHODS;   

DOI  :  10.1016/0377-0427(94)00074-9

来源: Elsevier

【 摘 要 】

The two-step methods proposed by Panovsky and Richardson (this journal, 1988) and analysed by Coleman and Booth (this journal, 1992) are shown to be equivalent to certain Runge-Kutta-Nystrom methods for differential equations of the form y'' = f(x, y). An important advantage of the new formulation is that it is no longer necessary to provide additional starting values at the beginning of a calculation or when the steplength or the order is changed; the new formulation is also more stable with respect to the propagation of rounding errors.

【 授权许可】

Free