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Fitted modifications of Runge‐Kutta pairs of orders 6(5)
Author(s) -
Medvedev Maxim A.,
Simos T. E.,
Tsitouras Ch.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5128
Subject(s) - runge–kutta methods , mathematics , dissipative system , phase lag , zero (linguistics) , function (biology) , dispersion (optics) , orbit (dynamics) , initial value problem , mathematical analysis , numerical analysis , physics , quantum mechanics , linguistics , philosophy , evolutionary biology , engineering , biology , aerospace engineering
Runge‐Kutta (RK) pairs sharing orders 6 and 5 are widely used for solving initial value problems. Thus, we consider the dispersion from a standard cyclic orbit as a function of frequency v and present a modification of a particular pair. Namely, we derive a zero‐dissipative pair with vanished phase lag and its first derivative. This modified pair outperforms the other Runge‐Kutta 6(5) pairs as illustrated with various numerical tests in oscillatory problems.