- #1
JulieK
- 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!
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!