This article is cited in 1 scientific paper (total in 1 paper)
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
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.
Runge–Kutta methods, stiff problems, order reduction.
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Computational Mathematics and Mathematical Physics, 2017, 57:7, 1124–1139
L. M. Skvortsov, “How to avoid accuracy and order reduction in Runge–Kutta methods as applied to stiff problems”, Zh. Vychisl. Mat. Mat. Fiz., 57:7 (2017), 1126–1141; Comput. Math. Math. Phys., 57:7 (2017), 1124–1139
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\paper How to avoid accuracy and order reduction in Runge--Kutta methods as applied to stiff problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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This publication is cited in the following articles:
L. M. Skvortsov, “Implicit Runge–Kutta methods with explicit internal stages”, Comput. Math. Math. Phys., 58:3 (2018), 307–321
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