Abstract:
The simplest equations are considered that simulate the behavior of various error components of Runge–Kutta methods. The expressions for the local and global errors are obtained. The minimization of these errors allows one to construct explicit and implicit methods that have an improved accuracy when solving stiff and differential-algebraic problems.
Keywords:
Runge–Kutta methods, still problems, differential-algebraic problems, order reduction phenomen.
This publication is cited in the following 8 articles:
L. M. Skvortsov, “Generalizations of the Stage Order of Runge–Kutta Methods”, Comput. Math. and Math. Phys., 64:12 (2024), 2796
L. M. Skvortsov, “Third- and fourth-order ESDIRK methods for stiff and differential-algebraic problems”, Comput. Math. Math. Phys., 46:5 (2022), 766–783
L. M. Skvortsov, “Implicit Runge–Kutta methods with explicit internal stages”, Comput. Math. Math. Phys., 58:3 (2018), 307–321
L. M. Skvortsov, “On implicit Runge–Kutta methods received as a result of inversion of explicit methods”, Math. Models Comput. Simul., 9:4 (2017), 498–510
L. M. Skvortsov, “How to avoid accuracy and order reduction in Runge–Kutta methods as applied to stiff problems”, Comput. Math. Math. Phys., 57:7 (2017), 1124–1139
L. M. Skvortsov, “Singly implicit diagonally extended Runge–Kutta methods of fourth order”, Comput. Math. Math. Phys., 54:5 (2014), 775–784
L. M. Skvortsov, “Runge–Kutta collocation methods for differential-algebraic equations of indices 2 and 3”, Comput. Math. Math. Phys., 52:10 (2012), 1373–1383
L. M. Skvortsov, “Explicit adaptive Runge–Kutta methods”, Math. Models Comput. Simul., 4:1 (2012), 82–91
Citation in format AMSBIB
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