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### Messages - Djirar

Pages: 1 [2]
16
##### Misc Math / Re: TT1Problem6
« on: October 15, 2012, 01:54:02 PM »
This is a reflection problem with Dirichlet boundary condition. The solution on the interval 0<x< âˆž  is given by:

$u(x,t) = \frac{1}{ \sqrt{4k \pi t}}\int_{0}^{\infty}{( e^{\frac{-(x-y)^2}{4kt}} - e^{\frac{-(x+y)^2}{4kt}} } )\phi(y) dy$

You can check page 59 of Strauss' book for more details.

17
##### Home Assignment 2 / Re: Problem4
« on: October 01, 2012, 09:00:18 PM »
problem 4

18
##### Home Assignment 1 / Problem 1
« on: September 25, 2012, 12:06:23 PM »
my solution to problem 1.

19
##### Home Assignment 1 / Re: Problem 5
« on: September 25, 2012, 11:04:27 AM »
Solution to problem 5

20
##### Home Assignment 1 / Re: Problem 5
« on: September 23, 2012, 08:59:09 PM »
Try using characteristic coordinates, I think it should work.

21
##### Home Assignment 1 / Re: Problem 5
« on: September 23, 2012, 02:45:20 PM »
I can't really see how part C of problem 5 is any different then a Cauchy problem, except for a change in coordinates and in the notes the initial conditions of the Goursat problem are given with respect to U only and not U_t .

Could someone please explain the differences between Goursat and Cauchy problems? thanks in advance.

22
##### Home Assignment 1 / Re: Problem 3
« on: September 22, 2012, 03:02:04 PM »
I got it, thank you for your help.

23
##### Home Assignment 1 / Re: Problem 3
« on: September 22, 2012, 01:52:35 PM »
I did use the method of characteristics, but I parametrized x and y in terms of s and integrated with respect to s . The thing is my solution doesn't depend on Y, is this ok ?

24
##### Home Assignment 1 / Problem 3
« on: September 22, 2012, 01:29:40 PM »
Hello,

For this question I managed to find a solution that satisfies the conditions, but that only depends on X and a constant.

In general, if I find a solution that satisfies all conditions is this solution correct regardless of the method used to find it?

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