ON SMOOTHING AND ORDER REDUCTION EFFECTS FOR IMPLICIT RUNGE-KUTTA FORMULAS

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:45

Article

BURRAGE, K ; CHAN, RPK

关键词: ORDER REDUCTION;    GAUSS METHODS;    SINGULAR PERTURBATION;    SYMMETRIZER;   

DOI  :  10.1016/0377-0427(93)90261-9

来源: Elsevier

【 摘 要 】

It is well known that many important classes of Runge-Kutta methods suffer an order reduction phenomenon when applied to certain classes of stiff problems. In particular, the s-stage Gauss methods with stage order s and order of consistency 2s behave like methods of order s when applied to the class of singularly perturbed problems. In this paper we will show that the process of smoothing can ameliorate this effect, when dealing with initial-value problems, by first studying the effect of smoothing on the standard Prothero-Robinson problem and then by extending the analysis to the general class of singularly perturbed problems.

【 授权许可】

Free