Gauss Legendre numerical intergration

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Gauss Legendre numerical intergration
The attachment file contain solved example
i dont know how he subsitute and why a2=2 done disappear in the answer
please expalin in details
 

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lurflurf

Homework Helper
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122
n=2
so
a2=1
 
107
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lurflurf

Homework Helper
2,417
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sure, we have from the handout and Gauss Legendre numerical integration
I=α1α1r12e^r1
1α2r12e^r2
2α1r22e^r1
2α2r22e^r2
now since n=2 we use
r1=-1/sqrt(3)~-0.57735026918962576450914878050196
r2=1/sqrt(3)~0.57735026918962576450914878050196
α1=1~1.000000000000000000000000000000000
αsub]2[/sub]=1~1.000000000000000000000000000000000

So just substitute in the values to find I
I=(4/3)cosh(1/sqrt(3))
=(1.000000000000000000000000000000000)(1.000000000000000000000000000000000)(-0.57735026918962576450914878050196)2e^-0.57735026918962576450914878050196
+(1.000000000000000000000000000000000)(1.000000000000000000000000000000000)(-0.57735026918962576450914878050196)2e^0.57735026918962576450914878050196
+(1.000000000000000000000000000000000)(1.000000000000000000000000000000000)(0.57735026918962576450914878050196)2e^-0.57735026918962576450914878050196
+(1.000000000000000000000000000000000)(1.000000000000000000000000000000000)(0.57735026918962576450914878050196)2e^0.57735026918962576450914878050196
=1.5617973919398203851893261344599

notice that only the values of α and r for n=2 are used
The values of α and r for other n are not used
In the handout all the ones were implied
 
Last edited:
107
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thank you brother
 

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