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Sixth‐order, P‐stable, Numerov‐type methods for use at moderate accuracies
Author(s) -
Medvedeva Marina A.,
Simos T. E.,
Tsitouras Ch.
Publication year - 2021
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.7233
Subject(s) - mathematics , type (biology) , algebraic number , reduction (mathematics) , order (exchange) , construct (python library) , function (biology) , mathematical analysis , geometry , computer science , ecology , finance , evolutionary biology , economics , biology , programming language
We consider a family of half‐implicit Numerov‐type methods for the numerical solution of the problem y ′′ = f ( x , y ) . These methods use off‐step points and waste four function evaluations (stages) per step. They attain sixth algebraic orders, while other methods of this type need five function evaluations per step. After we exploit this reduction in stages we construct a particular method and present various numerical tests on stiff periodic problems that justify its efficiency.