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¡Õ LOW MODES
HIGH MODES
1 0.8 0.6
λ(R )
0.4
J
0.0 0.2 0.4 0.6 0.8 1.0
0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0
2
4
v2 (mode k=2)
6
8
10
12
mode k n=19
Ç }&Öz|§ vmIyzl}tlv-v`oqIruk×
14
16
18
20
v15 (mode k=15)
¢
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0.5
λ (Rω J)
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0
ω =1.1
-0.5
ω =2/3
(UNSTABLE)
ω =1 -1
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mode k
ê$8dãVäå`ææ>=
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Ü¨Ý ûþ ÞÝöEDÝ°ßGàIá`ßÔõ û öF.HGI2|ðBýdá|ò û|þ ñBò!á`î6ñî°õ á|òß þ Ý3á°ô ûCû ï¸Þ úû7û ßà#Ý öÿKJVõML ÝÞÝ ß ßGàIÝ°ò û îï`ñßañ û îè êN{ëPOí3QSRTãaä ,-å æèç è ê9ëãVä ,-å æ7è ð>L Ý ûþ ß=á:ñîU. çWVYXPZ9ÿAÜ3Ý°á:ü Þ û î û ß Ý ßGàIá:ßZõ û ö[.:\]2ßGàIÝ ú Ý ßGà û ï þ Ý!ò û:ú Ý Þiødî#Þkß á þ ü/Ý^ï û ÝkÞ+î û ß&ò û îD:ÝöaôÝ;_Þkñîò!Ý)õ û ö+Þ û`ú Ý ? ðè ê 8#ãV9 ä ,-åæ7) è \W2ÿJ î Þ û:ú ÝlÞÝîIÞÝkðßà#Ý>`ökñVò!Ýß ûÊþ Ý>`#á:ñVï1õ û öªýdá|ò û|þ ñ&ß ûþ Ýáô ûCû ï Þ úlûCû ßGàIÝö$ñNÞálÞkü û Lï û Lî¸ñî¡ò û îD:Ý öaôÝîò!Ý û õ$ßGàIÝü û Lõ!öKÝ!÷ø#Ý îZò ù úû ï|Ý Þ ÿ
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600
ω=1 ω=2/3
Number of iterations
500 400 300 200 100 0
0
2
4
6
8
10
mode k
12
14
16
18
20
ZàIÝ1ô`öKái`IàÊÞKà û LÔÞlßà#Ýlî#ø úþ Ý ö û õbñß ÝöKá`ßañ û îIÞ1öÝ÷ødñöKÝ!ï°ß û öKÝ!ï:ø#ò!ÝlßGàIÝlßGàIݪá ú `ZüñßUø#ï|Ý õ Ý!á|ò!àÝökö û ö úû ï|Ý þ ùªá&õ á|òß û ö û õY|ÿ\ܨÝiÞÝ!Ý$ßGàIá`ßßà#ÝiÞkß=á:îïá:öKïªý-áò û|þ ñã'. ç@2Cæ û $ á:ü ô û ökñßà ú ðöÝ÷ødñöKÝ Þ ú á:î9ùÊñß=Ý öá:ßUñ û îIÞ°ß û Ýüñ ú ñîá`ß Ý3ßGàIÝ\à-ñ*ôàIÝ Þ!ß4õ!öKÝ!÷ ø#Ýîòù úlû ï|Ý Þÿ
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1 0.8 0.6
λ(RGS)
0.4 0.2 0
-0.4 -0.6 -0.8 -1
0
2
4
6
8
10
mode k n=19
v2 (mode k=2)
12
14
16
18
20
v15 (mode k=15)
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Ô$Õ Ö'×)Ø+Ù
n=19
200
Number of iterations
180 160 140 120 100 80 60 40 20 0
0
2
4
6
8
10
mode k
12
14
16
18
20
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1
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1 0.5
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0
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-0.5
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0
0.2
0.4
0.6
0.8
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1
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0.4
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1
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1.5
1.5
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0.5
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1
0.5
0
0.5
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1
1.5
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0.2
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1
1
0.5
0.5
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1
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Solution
Error
1.5
1.5
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1
0.5
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1
0.5
0
0.5
0
0.5
1
1
1.5
1.5 0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
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Error
1.5
1.5
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1
0.5
u(x)
1
0.5
0
0.5
0
0.5
1
1
1.5
1.5 0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
õcöK÷`ø¼ùÎúK ülý`þÿ& ! ÿL$M& ! ÿ.&8þ Solution
Error
1
1
0.5
0.5
u(x)-u h (x)
1.5
u(x)
1.5
0
0.5
0
0.5
1
1
1.5
1.5 0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
õcöK÷`ø¼ùÎúN ülý`þÿ þ ÿBLþ O"Ãÿ$% IýP&)(*&)+ÿQ!Solution
Error
1.5
1.5
u(x)-u h (x)
1
0.5
u(x)
1
0.5
0
0.5
0
0.5
1
1
1.5
1.5 0
0.2
0.4
0.6
0.8
1
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0
0.2
0.4
0.6
0.8
1
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6 8 10 12 14 0
5
10
15
20
25
# Iterations
1WbLUihce*jSQbXaXaseUlVyjY>VSlUQVgWStue[BWOp)Y>UlVfSj[B\>]xw6SjycdS)]1[S\!VY>bX] SB^MeUlbX]dcMVXWSQue*asVrb5cjlbo^ j \[BSB^>e*jS.z1WS[B\>]xw6SjycdS)]1[SMaSw6SaibLUnUW\>q']w6SjBUleUVgWSM]e*unBS)j_\pnbXVfSjYVybo\]U\>] VgWSJhi] SunSlUWz]1S_[BY>]VgWbX]*D\pVgWSn]e*unSjn\ pbXVfSjYVybo\]UbX]VXWSJhk]1SunSlUWdm#Y6U BS)bX]cY ! j\¡bXunY>VS)a5` j\ \>jlVrbo\>]1Y>a1Vf\tVgWS#Y>un\>e*]xV'\p[B\>u e*VY>Vrbo\>]1Y>a qi\>jbX]w>\>a5w6SB^!z
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log ||r||
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3 4
10
5 6
2 levels 3 levels 4 levels 5 levels 6 levels
7 8 9 10
1
2
3
4
5
6
7
8
9
10
# Iterations
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# Iterations
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