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Gauss Legendre numerical intergration

  1. Oct 29, 2012 #1
    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
     

    Attached Files:

  2. jcsd
  3. Oct 29, 2012 #2

    lurflurf

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    n=2
    so
    a2=1
     
  4. Oct 30, 2012 #3
    What about a1=2
    doent apper
    could u explain more pls
     
  5. Oct 31, 2012 #4

    lurflurf

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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: Oct 31, 2012
  6. Oct 31, 2012 #5
    thank you brother
     
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