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Truncation Error and Second Order Accuracy.

  1. May 3, 2014 #1
    By combining the two equations i should be able to solve for u' and get rid of u'':

    u_(i-1) = u_i + (-h)*u' + 1/2 * (-h)^2 * u'' + O(h^4)

    u_(i-2) = u_i + (-2h)*u' + 1/2 * (-2h)^2 * u'' + O(h^4)

    But i keep getting stuck and can't come up with the answer below.

    Can anyone help me please.

    u'=((3u_i-4u_(i-1)+u_(i-2))/2h)+O(h^4)
     
  2. jcsd
  3. May 3, 2014 #2

    lurflurf

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    multiply the first equation by -4

    -4u_(i-1) = -4u_i + (4h)*u' - 1/2 * (-2h)^2 * u'' + O(h^4)

    u_(i-2) = u_i + (-2h)*u' + 1/2 * (-2h)^2 * u'' + O(h^4)

    now solve for u'
     
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