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Fourth‐order accurate one‐step integration methods with large imaginary stability limits
Author(s) -
Kinnmark Ingemar P. E.,
Gray William G.
Publication year - 1986
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690020106
Subject(s) - mathematics , stability (learning theory) , the imaginary , limit (mathematics) , order (exchange) , function (biology) , runge–kutta methods , mathematical analysis , calculus (dental) , differential equation , computer science , medicine , psychology , dentistry , finance , machine learning , evolutionary biology , economics , psychotherapist , biology
Abstract One‐step integration methods of fourth‐order accuracy using an odd number of function evaluations K , to solve dy/dt = A · y , are proposed. These methods have an imaginary stability limit \documentclass{article}\pagestyle{empty}\begin{document}$ S_{1\;} = \sqrt {(K - 1)^2 - 4} $\end{document} . In the case K = 5 the Kutta‐Merson method results.