- #1

Mattbringssoda

- 16

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## Homework Statement

[/B]Determine the Green's functions for the two-point boundary value problem u''(x) = f(x) on 0 < x < 1 with a Neumann boundary condition at x = 0 and a Dirichlet condition at x = 1, i.e, find the function G(x; x) solving

u''(x) = delta(x - xbar) (the Dirac delta function); u'(0) = 0; u(1) = 0

and the functions G_0 (x) solving

u''(x) = 0; u'(0) = 1; u(1) = 0

and G_1(x) solving

u''(x) = 0; u'(0) = 0; u(1) = 1:

## Homework Equations

## The Attempt at a Solution

Right now I'm most concerned with the first part of the problem, the main Green's function G(x,x) solving: u''(x) = delta(x - xbar) (the dirac delta function); u'(0) = 0; u(1) = 0.

I'm stuck because we're using these functions to make discreet approximations to boundary value problems via matrices, so I assume the functions have to be linear.

However, u'(0) = 0 would have to be of some form u'(x) = x, so the solution would have to be a non-linear term, along the lines of u(x) = x^c. That doesn't seem right in light of what we've been learning...so I don't know what to do here...

Any help is much appreciated!