Derivation of three-derivative Runge-Kutta methods
Küçük Resim Yok
Tarih
2017
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
We introduce an algorithm for a numerical integration of ordinary differential equations in the form of y' = f(y). We extend the two-derivative Runge-Kutta methods (Chan and Tsai, Numer. Algor. 53, 171-194, 2010) to three-derivative Runge-Kutta methods by including the third derivative . We present an approach based on the algebraic theory of Butcher (Math. Comp. 26, 79-106, 1972) and the series theory of Hairer and Wanner (Computing 13, 1-15 (1974)) combined with the methodology of Chan and Chan (Computing 77(3), 237-252, 2006). In this study, special explicit three-derivative Runge-Kutta methods that possess one evaluation of first derivative, one evaluation of second derivative, and many evaluations of third derivative per step are introduced. Methods with stages up to six and of order up to ten are presented. The numerical calculations have been performed on some standard problems and comparisons made with the accessible methods in the literature.
Açıklama
Anahtar Kelimeler
Two-derivative Runge-Kutta methods, Rooted trees, Multi-derivative Runge-Kutta methods, Order conditions
Kaynak
Numerical Algorithms
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
74
Sayı
1
