On smoothing and order reduction effects for implicit Runge Kutta formulae [CAM 1275]

• Autores: Kevin Burrage, R.P.K. Chan
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Nº 1, 1993, pág. 17
• Idioma: inglés
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• Resumen

  • 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.