This preview shows page 1. Sign up to view the full content.
Unformatted text preview: w C hp:
n
h
51 Ideally, we would like to compute a step size hOPT so that Cnhp :
OPT
Eliminating the coe cient Cn between the two equations
hp
OPT
~ nkw hp+1
kd
or
h 1=p :
hOPT
~
h
kdnkw (3.5.9a) The error estimates are based upon an asymptotic analysis and are, thus, not completely reliable. Therefore, it is best to include safety factors such as
(
"
#)
1=p
hOPT = h min M AX max M IN s ~
:
(3.5.9b) kdnkw The factors M AX and M IN limit the maximum step size increase and decrease, respectively, while s tends to make step size changes more conservative. Possible choices of the
parameters are M AX = 5, M IN = 0:1, and s = 0:9. Step size control based on either
(3.5.8a) or (3.5.8c) works similarly. In general, the user must also provide a maximum
step size hMAX so that the code does not miss interesting features in the solution.
Selection of the initial step size is typically left to the user. This can be somewhat
problematical and several automatic initial step size procedures are under investigation.
One automatic...
View
Full
Document
This document was uploaded on 03/16/2014 for the course CSCI 6820 at Rensselaer Polytechnic Institute.
 Spring '14
 JosephE.Flaherty

Click to edit the document details