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Hybrid, phase–fitted, four–step methods of seventh order for solving x ″ ( t ) = f ( t , x )
Author(s) -
Medvedev Maxim A.,
Simos T. E.,
Tsitouras Ch.
Publication year - 2019
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.5495
Subject(s) - mathematics , order (exchange) , algebraic number , set (abstract data type) , variable (mathematics) , phase (matter) , value (mathematics) , initial value problem , mathematical analysis , statistics , computer science , chemistry , organic chemistry , finance , economics , programming language
A four‐step method of seventh algebraic order is presented. It is tuned for addressing the special second order initial value problem. The new method is hybrid, explicit, and uses three stages per step. In addition is phase fitted. In consequence it uses variable coefficients that depend on the magnitude of the step‐size. We also present numerical tests on a set of standard problems that illustrate the efficiency of the derived method over older ones given in the relevant literature.