Unformatted text preview: w C hp:
51 Ideally, we would like to compute a step size hOPT so that Cnhp :
Eliminating the coe cient Cn between the two equations
~ nkw hp+1
h 1=p :
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
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.
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- Spring '14
- Numerical Analysis, yn, Tn, Numerical ordinary differential equations