Fitted modifications of Runge‐Kutta pairs of orders 6(5) | Zendy

Medvedev Maxim A. | Zendy; Simos T. E. | Zendy; Tsitouras Ch. | Zendy

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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.

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