Hello

I have example to resolve:

where

Anyone to help me?

Printable View

- Aug 27th 2012, 10:09 AManka0501Partial differential equation
Hello

I have example to resolve:

where

Anyone to help me? - Aug 27th 2012, 10:59 AMMaxJasperRe: Partial differential equation
You can use these two beauties:

=

- Aug 28th 2012, 01:38 AMJJacquelinRe: Partial differential equation
Hi !

Changing the cartesian coordinates system to hyperbolic system leads to a very simple PDE. So, the general solution is obtained (in attachment).

Then the condition u(1,y)=1+y will be easy to apply in order to express the particular solution. - Aug 28th 2012, 01:40 AManka0501Re: Partial differential equation
I don't understand...Maybe this is not true.

- Aug 28th 2012, 01:46 AManka0501Re: Partial differential equation
JJacquelin how you get x and y?

- Aug 28th 2012, 02:04 AMJJacquelinRe: Partial differential equation
I quite not understand your question

x = rho*cosh(theta) and y = rho*sinh(theta)

The inverse is : rho = sqrt(x²-y²) and theta = argtanh(y/x)

This is the usual relationship between cartesian coordinates and hyperbolic coordinates. - Aug 28th 2012, 03:26 AMJJacquelinRe: Partial differential equation
By the way, a much simpler method consists in :

Let u(x,y) = (x+y)*v(x,y)

Binging back into the PDE leads to y*(dv/dx)+x*(dv/dy) = 0

which is very easy to solve. - Aug 28th 2012, 04:36 AManka0501Re: Partial differential equation

- shooting fish in a barrel

I case study new method, which seems easier. I've done this example, but I got the another answer.

After that I talled t and L

If you understand this method, plese give me the answer it is correct? - Aug 28th 2012, 04:50 AMJJacquelinRe: Partial differential equation
Sorry, in fact, I didn't read your method.

I just bing back your result u(x,y) into the PDE. It doesn't aggree.

Clue : The final solution of your problem is very simple : u(x,y) = x+y - Aug 28th 2012, 05:26 AManka0501Re: Partial differential equation
Maybe I give in....or could you give me advice in which book I find this method or where (link)?

- Aug 28th 2012, 06:55 AManka0501Re: Partial differential equation
I understand your solution, thanks for your help, but I have one question, when I have to make a parametrization?

- Aug 28th 2012, 07:37 AMJJacquelinRe: Partial differential equation
I couldn't give a general answer.

As many methods : try and see if it allows simplifications or not. - Aug 28th 2012, 10:09 AManka0501Re: Partial differential equation
Ok, thank you