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Exercises Chapter 6 |
JLMARTIN
Joined: 30 Jul 2012
Posts: 14
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Posted: Sun Sep 23, 2012 5:33 pm Post subject: |
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understood!
thank you Daniel |
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Cuchulainn
Joined: 18 Dec 2006
Posts: 607
Location: Amsterdam, the Netherlands
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Posted: Sun Sep 16, 2012 6:45 pm Post subject: |
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Hi JL,
Since this is 1 factor then the norm just becomes the absolute value of df/dy.
Problem is we don't know y. So some heuristics.
Ex.
say df/fy = 1/y^2. let's assume y > 0.7 on [0, 0.2] (normally see this from iterated values of y_{k} )
then h < 2y^2 on interval [0, 0.2]. Then convergence if h < 2(0.7)^2.
So, something similar in you case.
hth
Daniel |
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JLMARTIN
Joined: 30 Jul 2012
Posts: 14
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Posted: Sun Sep 09, 2012 5:46 pm Post subject: |
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Thank you Daniel for your help
for the first test case, I'm using
T=3
h=0.01
Tolerance=0.001
max iterations=1000
If I use 6.43, and given that I'm using the test case 2, what would be the condition for the convergence? If I use the L2 norm, isnt df/dy=(1/3)*t*y^(-2/3)? but in which should I apply the condicion ||df/dy||*h<2?
Regards |
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Cuchulainn
Joined: 18 Dec 2006
Posts: 607
Location: Amsterdam, the Netherlands
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Posted: Mon Aug 20, 2012 5:57 pm Post subject: |
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Hi JL,
1.- in the first test case, you give as initial condition the value in t=1: y(1)=1. I find problems when dealing with it, since I can't apply the algorigthms... how am I supposed to deal with it?
DD In principles it's just a different start point. Can you take t' = t - 1.
2.- While with test case number 2 I find that the exact solution is prety similar to those offered by the numerical methods applied (i.e predictor-corrector and runge-kutta orders 2 and 4), in the test case 1, when I choose a large T (like T=3) the exact solution goes way quickly...
DD The exact solution goes to the value 2 when T gets big.
How many mesh points are you taking?
Adaptive meshing would use eq. (6.43) to find the correct meshe size. |
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Cuchulainn
Joined: 18 Dec 2006
Posts: 607
Location: Amsterdam, the Netherlands
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Posted: Thu Aug 09, 2012 11:56 am Post subject: |
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Hi JL,
Sorry, I was away. I will get back to you.
D |
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JLMARTIN
Joined: 30 Jul 2012
Posts: 14
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Posted: Thu Aug 09, 2012 7:29 am Post subject: |
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Hi
no news? |
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JLMARTIN
Joined: 30 Jul 2012
Posts: 14
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Posted: Mon Jul 30, 2012 3:26 pm Post subject: Exercises Chapter 6 |
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hi Daniel
I have a couple of questions regarding chapter 6 exercises, I hope you can help me
1.- in the first test case, you give as initial condition the value in t=1: y(1)=1. I find problems when dealing with it, since I can't apply the algorigthms... how am I supposed to deal with it?
2.- While with test case number 2 I find that the exact solution is prety similar to those offered by the numerical methods applied (i.e predictor-corrector and runge-kutta orders 2 and 4), in the test case 1, when I choose a large T (like T=3) the exact solution goes way quickly...
is this the expected behaviour?
Thank you for your help |
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