TY - JOUR
T1 - Starting procedures for general linear methods
AU - Califano, G.
AU - Izzo, G.
AU - Jackiewicz, Zdzislaw
N1 - Funding Information:
The work of this author was partially supported by INdAM-GNCS.
Publisher Copyright:
© 2017 IMACS
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/10
Y1 - 2017/10
N2 - We present a systematic approach to the construction of starting procedures for general linear methods (GLMs) of order p and stage order q=p. Order conditions for starting procedures based on the generalized Runge–Kutta (RK) are derived using the theory of rooted trees, elementary differentials, and elementary weights, and examples of generalized RK formulas are given up to the order p=4.
AB - We present a systematic approach to the construction of starting procedures for general linear methods (GLMs) of order p and stage order q=p. Order conditions for starting procedures based on the generalized Runge–Kutta (RK) are derived using the theory of rooted trees, elementary differentials, and elementary weights, and examples of generalized RK formulas are given up to the order p=4.
KW - General linear methods
KW - Generalized Runge–Kutta methods
KW - Order conditions
KW - Starting procedures
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U2 - 10.1016/j.apnum.2017.05.009
DO - 10.1016/j.apnum.2017.05.009
M3 - Article
AN - SCOPUS:85020040132
SN - 0168-9274
VL - 120
SP - 165
EP - 175
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -