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For 3<br />
<br />
2 4<br />
y2 = b0 + b1<br />
( ) 2<br />
The boundary conditions at = <br />
2 are y1 = a2 <br />
2<br />
and<br />
Also<br />
or<br />
b0 + b1 <br />
2<br />
( ) 2<br />
= a2 <br />
2<br />
0 = a2 ( 2 ) 2<br />
+ b0 + b1 <br />
2<br />
y'2 = b1 = a2<br />
0 = a2 b1<br />
For 3 5<br />
<br />
4 4<br />
y3 = c0 + c1 + c2 2<br />
y'3 = c1 + 2c2<br />
y"3 = 2c2<br />
- 331 -<br />
and y'1 = 2a2 <br />
2 = a2 . Then<br />
The boundary conditions at = 3<br />
4 are y2 = a2 <br />
4 + ( ) = a2 3<br />
+<br />
4 4<br />
Also, at = 5<br />
4 , y3 =1.5 and y'3 = 0 . Then, matching the conditions,<br />
2<br />
y3 = a2<br />
2 = c0 +c1 3<br />
4<br />
y'3 = c1 + 2c2 3<br />
= a2<br />
4<br />
1.5 = c0 + c1 5 5<br />
+c2<br />
4 4<br />
( ) 2<br />
3<br />
+ c2( 4 ) 2<br />
y'3 = c1 + 2c2 5<br />
4 = 0<br />
The boundary condition equations can be written as:<br />
( )<br />
= a2 2<br />
2 and y'2 = a2 .
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