TY - JOUR
T1 - Algebraically stable diagonally implicit general linear methods
AU - Hewitt, Laura L
AU - Hill, Adrian T
PY - 2010/6
Y1 - 2010/6
N2 - This paper concerns algebraically stable diagonally implicit general linear methods, intended for stiff differential equations. The first step in the construction of such methods is to apply the order theory from the series of papers by Butcher and Jackiewicz. The order theory and structural assumptions leave a number of free parameters, which may be chosen to make the method both simple and algebraically stable. Here, this choice is made by applying new sufficient conditions for algebraic stability. Methods of 2 steps and 2 stages are constructed with stage order 2, and total order up to 4.
AB - This paper concerns algebraically stable diagonally implicit general linear methods, intended for stiff differential equations. The first step in the construction of such methods is to apply the order theory from the series of papers by Butcher and Jackiewicz. The order theory and structural assumptions leave a number of free parameters, which may be chosen to make the method both simple and algebraically stable. Here, this choice is made by applying new sufficient conditions for algebraic stability. Methods of 2 steps and 2 stages are constructed with stage order 2, and total order up to 4.
KW - algebraic stability
KW - DIMSIMs
KW - stiff problems
KW - general linear methods
UR - http://www.scopus.com/inward/record.url?scp=77953135339&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1016/j.apnum.2010.03.004
U2 - 10.1016/j.apnum.2010.03.004
DO - 10.1016/j.apnum.2010.03.004
M3 - Article
SN - 0168-9274
VL - 60
SP - 629
EP - 636
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 6
ER -