TY - JOUR
T1 - Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations
AU - Jackiewicz, Zdzislaw
AU - Vermiglio, R.
AU - Zennaro, M.
N1 - Funding Information:
The work of the first author was supportedb y the National Science Foundationu ndergrant NSF DMS-9208048.
PY - 1995/1
Y1 - 1995/1
N2 - We study a class of variable stepsize general linear methods for the numerical solution of ordinary differential equations. These methods provide an alternative to the Nordsieck technique of changing the stepsize of integration. Order conditions are derived using a recent approach by Albrecht and examples of methods are given which are appropriate for stiff or nonstiff systems in sequential or parallel computing environments. A construction of variable stepsize continuous methods is also described which is facilitated by adding, in general, one extra external stage. Numerical experiments are presented which indicate that the implementation based on variable stepsize formulation is more accurate and more efficient than the implementation based on Nordsieck's technique for second-order DIMSIMs of type 1.
AB - We study a class of variable stepsize general linear methods for the numerical solution of ordinary differential equations. These methods provide an alternative to the Nordsieck technique of changing the stepsize of integration. Order conditions are derived using a recent approach by Albrecht and examples of methods are given which are appropriate for stiff or nonstiff systems in sequential or parallel computing environments. A construction of variable stepsize continuous methods is also described which is facilitated by adding, in general, one extra external stage. Numerical experiments are presented which indicate that the implementation based on variable stepsize formulation is more accurate and more efficient than the implementation based on Nordsieck's technique for second-order DIMSIMs of type 1.
KW - General linear method
KW - Interpolants
KW - Order conditions
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U2 - 10.1016/0168-9274(94)00057-N
DO - 10.1016/0168-9274(94)00057-N
M3 - Article
AN - SCOPUS:0007082106
SN - 0168-9274
VL - 16
SP - 343
EP - 367
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 3
ER -