Premium
Trigonometric fitted, eighth‐order explicit Numerov‐type methods
Author(s) -
Berg Dmitry B.,
Simos T. E.,
Tsitouras Ch.
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.4711
Subject(s) - mathematics , trigonometry , type (biology) , dissipative system , order (exchange) , base (topology) , matlab , set (abstract data type) , nonlinear system , mathematical analysis , computer science , ecology , physics , finance , quantum mechanics , economics , biology , programming language , operating system
We consider the integration of the special second‐order initial value problem of the formy′′= f ( x , y ) . A recently introduced family of 7 stages, eighth‐order methods, sharing constant coefficients, is used as base. This family is properly modified to derive phase fitted and zero dissipative methods (ie, trigonometric fitted) that are best suited for integrating oscillatory problems. Numerical tests over a set of problems shows enhanced performance when the purely linear part of the problems is rather large in comparison with the rest of nonlinear parts. An appendix implementing a MATLAB listing with the coefficients of the new method is also given.