Form of function over interval

  • Thread starter JulieK
  • Start date
  • #1
50
0
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!
 

Attachments

  • aaaa.png
    aaaa.png
    1.3 KB · Views: 324

Answers and Replies

  • #2
50
0
I should have added

[itex]g(A,B)=g(A,c)=g(c,d)=g(d,e)=g(e,B)=E[/itex]
 
  • #3
mathman
Science Advisor
7,942
496
You need to describe the relationship between f and g.
 
  • #4
50
0
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!
 

Related Threads on Form of function over interval

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
1
Views
2K
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
Replies
1
Views
933
Replies
4
Views
2K
Top