This article is cited in 8 papers

How to avoid accuracy and order reduction in Runge–Kutta methods as applied to stiff problems

L. M. Skvortsov

Bauman State Technical University, Moscow, Russia

Abstract: The solution of stiff problems is frequently accompanied by a phenomenon known as order reduction. The reduction in the actual order can be avoided by applying methods with a fairly high stage order, ideally coinciding with the classical order. However, the stage order sometimes fails to be increased; moreover, this is not possible for explicit and diagonally implicit Runge–Kutta methods. An alternative approach is proposed that yields an effect similar to an increase in the stage order. New implicit and stabilized explicit Runge–Kutta methods are constructed that preserve their order when applied to stiff problems.

Key words: Runge–Kutta methods, stiff problems, order reduction.

UDC: 519.62

Received: 17.09.2015
Revised: 17.10.2016

DOI: 10.7868/S0044466917070134

 English version: Computational Mathematics and Mathematical Physics, 2017, 57:7, 1124–1139

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