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Interpolants for sixth‐order Numerov‐type methods
Author(s) -
Alolyan Ibraheem,
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.5848
Subject(s) - mathematics , interpolation (computer graphics) , type (biology) , set (abstract data type) , order (exchange) , runge–kutta methods , mathematical analysis , numerical analysis , motion (physics) , computer science , ecology , finance , artificial intelligence , economics , biology , programming language
The classical four‐stage family of explicit sixth‐order Numerov‐type method is considered. We provide two kinds of interpolants: (a) a three‐step interpolation based on all available data at mesh points and (b) a local interpolant (ie, two steps) that is constructed after solving scaled equations of condition. These latter equations are explained and provided here. Applying these interpolants in a set of tests, we conclude that they produce global errors of the same magnitude with the underlying method.