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Explicit, two‐stage, sixth‐order, hybrid four‐step methods for solving y ′ ′ ( x ) = f ( x , y )
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.5211
Subject(s) - mathematics , truncation error , phase lag , truncation (statistics) , nonlinear system , order (exchange) , calculus (dental) , statistics , finance , economics , medicine , physics , dentistry , quantum mechanics
A purely interpolatory approach is applied for derivation of methods mentioned in the title. Four parameters remain free and are enough for presenting a method with minimal truncation error and another one of high phase‐lag order. After extended numerical tests in various nonlinear and oscillatory problems, it seems that the new methods outperform similar methods found in the literature.