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Form of function over interval

  1. Dec 1, 2013 #1
    I know [itex]y[/itex] is a function of [itex]x[/itex] [i.e. [itex]y=f\left(x\right)[/itex]]
    with two known boundary conditions, that is [itex]f\left(x=A\right)=C[/itex]
    and [itex]f\left(x=B\right)=D[/itex] where [itex]C[/itex] and [itex]D[/itex] are known constants
    (please see figure). I do not know the form of this function and therefore
    I am trying to find the form of [itex]y[/itex] as a function of [itex]x[/itex] over the
    whole interval [itex]A<x<B[/itex]. I have an additional condition that is if
    I discretize the interval I can obtain the folowing relation


    where [itex]g[/itex] is a known function of the given arguments and [itex]E[/itex] is
    a known constant. I think this problem can be solved by using the
    variational principle possibly with the use of Lagrange multipliers.
    I did some initial attempts but I am not sure about the results. Can
    you suggest a method (variational or not) that can solve this problem
    so that we can obtain the form of [itex]y[/itex] as a function of [itex]x[/itex] over
    the whole interval.

    Many thanks in advance!

    Attached Files:

  2. jcsd
  3. Dec 1, 2013 #2
    I should have added

  4. Dec 1, 2013 #3


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    Science Advisor

    You need to describe the relationship between f and g.
  5. Dec 1, 2013 #4
    I made a mistake in the problem description. The additional condition is:


    Sorry about this!
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