Here is another set of L-Stable coefficients for the
Rosenbrock generalized method, as presented in Hairer & Wanner. The Gamma value for the L-Stable coefficients is 0.572. The coefficients have
been obtained from here.
A31= 0.1867943637803922E1
A32= 0.2344449711399156
C21=-0.7137615036412310E1
C31= 0.2580708087951457E1
C32= 0.6515950076447975
C41=-0.2137148994382534E1
C42=-0.3214669691237626
C43=-0.6949742501781779
B1= 0.2255570073418735E1
B2= 0.2870493262186792
B3= 0.4353179431840180
B4= 0.1093502252409163E1
E1=-0.2815431932141155
E2=-0.7276199124938920E-1
E3=-0.1082196201495311
E4=-0.1093502252409163E1
GAMMA= 0.5728200000000000
C2= 0.1145640000000000E1
C3= 0.6552168638155900
D1= 0.5728200000000000
D2=-0.1769193891319233E1
D3= 0.7592633437920482
D4=-0.1049021087100450
First, I would like to congratulate Anand Srinivasan on this numerical integration blog and thank him for his time and effort to post his thoughts with a such regularity! When Anand told me about the blog a month ago, I have been reading all posts every weekend and enjoyed doing so.
ReplyDeleteMany years ago, I did some developments on Boundary Element Methods and also some work on Finite Element Methods, so had to do a lot of work related to numerical integration. I wish I had seen some of the posts before, as these ideas might have been of real help for my tedious work back then. At least, I could have tried some things that Anand discusses here just to see how they would work out for temporal integration rather that considering a convolution algorithm, for example.
Keep up a nice work, Anand!
Mikhail Grigoriev