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A BPC can be characterized by adding two extra constraints G1=0 and G2=0 to (50) where G1 and G2 are the Branch Point test functions. The complete BVP defining a BPC point using the minimal extended system is
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ì ï ï ï í
ï ï ï î
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| |
| |
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ó õ
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1
0
|
áx(t), |
×
x
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old
|
(t) ñdt |
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|
|
| | (86) |
|
where
is defined by requiring
N |
æ ç
ç è
|
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ö ÷
÷ ø
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= |
æ ç ç ç
ç ç ç è
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|
ö ÷ ÷ ÷
÷ ÷ ÷ ø
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. |
| (87) |
Here v1 and v2 are functions, G1 and G2 are scalars and
where the bordering operators v11,v21, function w01, vector w02 and scalars v12,v22,v13,v23 and w03 are chosen so that N is nonsingular [7][8].