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Science Forum Index » Math - Numerical Analysis Forum » Runge-kutta stability
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| Guest |
 Posted: Sun Mar 11, 2007 5:28 pm |
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Hi,
suppose that the stability function of a 2-level rk method is
R(z) = [z^2 +6z + 12] / [z^2 - 6z + 12]
In order to be stable, |R(z)| <= 1. How can i check this?
I have calculated the R(z) function, but now I'am having some problem
with that inequalities
Thank you |
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| Peter Spellucci |
| Posted: Mon Mar 12, 2007 3:45 am |
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Guest
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In article <1173652136.673204.63950@j27g2000cwj.googlegroups.com>,
kingpin@freemail.it writes:
Quote: Hi,
suppose that the stability function of a 2-level rk method is
R(z) = [z^2 +6z + 12] / [z^2 - 6z + 12]
In order to be stable, |R(z)| <= 1. How can i check this?
I have calculated the R(z) function, but now I'am having some problem
with that inequalities
Thank you
homework?
hint:
abs(R(z)) < 1 <=>
abs(z^2+6z+12) < abs(z^2 -6z +12) <=>
abs(z^2+6z+12)^2 < abs(z^2-6z+12)^2
use
abs(expr)^2 = Re(expr)^2+Im(expr)^2
getting finally an inequality involving Re(z) and Im(z)
hth
peter |
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