TY - JOUR
T1 - A nonlinear optimization approach to the construction of general linear methods of high order
AU - Butcher, J. C.
AU - Jackiewicz, Zdzislaw
AU - Mittelmann, Hans
N1 - Funding Information:
* Corresponding author. E-mail: jackiewi@math.la.asu.edu. grant NSF DMS-9208048 ’ Work was assisted by the Marsden Fund of New Zealand. ’ Partially supported by the National Science Foundation under grant NSF DMS-9403716.
PY - 1997/7/8
Y1 - 1997/7/8
N2 - We describe the construction of diagonally implicit multistage integration methods of order and stage order p = q = 7 and p = q = 8 for ordinary differential equations. These methods were obtained using state-of-the-art optimization methods, particularly variable-model trust-region least-squares algorithms.
AB - We describe the construction of diagonally implicit multistage integration methods of order and stage order p = q = 7 and p = q = 8 for ordinary differential equations. These methods were obtained using state-of-the-art optimization methods, particularly variable-model trust-region least-squares algorithms.
KW - A-stability
KW - General linear method
KW - L-stability
KW - Least-squares minimization
KW - Ordinary differential equation
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U2 - 10.1016/S0377-0427(97)00039-3
DO - 10.1016/S0377-0427(97)00039-3
M3 - Article
AN - SCOPUS:0031559380
SN - 0377-0427
VL - 81
SP - 181
EP - 196
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -