Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    [itex]g(A,c)=g(c,d)=g(d,e)=g(e,B)=E[/itex]

    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

    [itex]g(A,B)=g(A,c)=g(c,d)=g(d,e)=g(e,B)=E[/itex]
     
  4. Dec 1, 2013 #3

    mathman

    User Avatar
    Science Advisor
    Gold Member

    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:

    [itex]g(y(A),y(B))=g(y(A),y(c))=g(y(c),y(d))=g(y(d),y(e))=g(y(e),y(B))=E[/itex]

    Sorry about this!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook