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Modified two‐step hybrid methods for the numerical integration of oscillatory problems
Author(s) -
Monovasilis T.,
Kalogiratou Z.,
Ramos Higinio,
Simos T. E.
Publication year - 2017
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.4386
Subject(s) - mathematics , numerical integration , numerical analysis , constant (computer programming) , variable (mathematics) , initial value problem , order (exchange) , mathematical analysis , computer science , finance , economics , programming language
The construction of modified two‐step hybrid methods for the numerical solution of second‐order initial value problems with periodic or oscillatory behavior is considered. The coefficients of the new methods depend on the frequency of each problem so that the harmonic oscillatory′ ′= − w 2 y is integrated exactly. Numerical experiments indicate that the new methods are more efficient than existing methods with constant or variable coefficients. Copyright © 2017 John Wiley & Sons, Ltd.