# Triple Integral - Volterra equation problem

• Dec 8th 2010, 07:13 AM
ark600
Triple Integral - Volterra equation problem
Here's the problem:

y'''(x) = f(x) subject to the conditions y(0)=y(1)=y(2)=0.

Perform three integrations to show that a solution may be written

y(x) = $\int_{0}^{2}L(x,t)f(t)dt$

Determine L(x,t).

My attempt:

After triple integration I get

y(x) = $Ax +Bx^2 +\frac{1}{2}\int_{0}^{x}(x-t)^2f(t)dt$

where A and B are constants which I've determined but won't write here.

Anyway, I don't see how this can be converted to find the desired L(x,t)
(I'm assuming my triple integration is correct- I think it is)
• Dec 8th 2010, 07:45 AM
TheEmptySet
Quote:

Originally Posted by ark600
Here's the problem:

y'''(x) = f(x) subject to the conditions y(0)=y(1)=y(2)=0.

Perform three integrations to show that a solution may be written

y(x) = $\int_{0}^{2}L(x,t)f(t)dt$

Determine L(x,t).

My attempt:

After triple integration I get

y(x) = $Ax +Bx^2 +\frac{1}{2}\int_{0}^{x}(x-t)^2f(t)dt$

where A and B are constants which I've determined but won't write here.

Anyway, I don't see how this can be converted to find the desired L(x,t)
(I'm assuming my triple integration is correct- I think it is)

The form of your solution is correct, and if you have solve for A and B you are done!
• Dec 8th 2010, 08:59 AM
ark600
I couldn't see the wood for the trees: the question just asked for a solution.
I just stick x=2 in.
LOL
Cheers