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Explicit hybrid six–step, sixth order, fully symmetric methods for solving y ″ = f ( x , y )
Author(s) -
Fang Jie,
Liu Chenglian,
Hsu ChiehWen,
Simos Theodore E.,
Tsitouras Charalampos
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.5585
Subject(s) - mathematics , linear multistep method , order (exchange) , interval (graph theory) , numerical analysis , interpolation (computer graphics) , set (abstract data type) , type (biology) , mathematical analysis , combinatorics , differential equation , computer science , animation , differential algebraic equation , ordinary differential equation , ecology , computer graphics (images) , finance , economics , biology , programming language
A family of explicit, fully symmetric, sixth order, six‐step methods for the numerical solution of y ′′ = f ( x , y ) is studied. This family wastes two function evaluations per step and can be derived through interpolation techniques. An interval of periodicity is possessed and the phase lag is of high order. Numerical instabilities usually present in such type of multistep methods were circumvented. We conclude with extended numerical tests over a set of problems justifying our effort of dealing with the new methods.