# How to solve a partial differential equation??

• May 2nd 2008, 04:05 PM
WangTaoSG
How to solve a partial differential equation??
Dear All,

How to solve a partial differential equation? Don't know how to write math equation so have to put as attachment, hope you don't mind.

Appreciate your helps very much!!!
• May 2nd 2008, 11:05 PM
mr fantastic
Quote:

Originally Posted by WangTaoSG
Dear All,

How to solve a partial differential equation? Don't know how to write math equation so have to put as attachment, hope you don't mind.

Appreciate your helps very much!!!

The prefered approach will depend on what f(x, y) is. You say it's known, it might help to let us know too.
• May 3rd 2008, 04:43 AM
WangTaoSG
Is there a general way of solving any F(x,y)?
Hi,

I am looking for a general solution so you may assume F(x,y) be any two-dimentional function. Does the solution rely very much on the form of F(x,y)? Is there a general way of solving such problem?

But you may assume F(x,y)=x^2+y^2

Thanks very much for your help!
• May 3rd 2008, 04:05 PM
mr fantastic
Quote:

Originally Posted by WangTaoSG
Hi,

I am looking for a general solution so you may assume F(x,y) be any two-dimentional function. Does the solution rely very much on the form of F(x,y)? Is there a general way of solving such problem?

But you may assume F(x,y)=x^2+y^2

Thanks very much for your help!

$\displaystyle \frac{\partial w}{\partial x} \, \frac{\partial w}{\partial y} = F(x, y)$.

If F(x, y) had the seperable form F(x, y) = a(x) b(y), for example $\displaystyle F(x, y) = x^2 y^2$, then you could assume a solution of the form w = X(x) Y(y) and it's blue sky.

For $\displaystyle F(x, y) = x^2 + y^2$ things are less straightforward.

I haven't really had a close look - a suggestion that might work is to use a transform technique eg Fourier or Laplace. Although the success of this might depend on the given boundary conditions (which have not been mentioned so far).

If I have the time, I will try to take a closer look if no-one else does.
• May 3rd 2008, 04:29 PM
WangTaoSG
Will try your suggestion
Hi fantastic,

Transform method might work, will try. at first i thought it is easyas the equation is so simple, but seems it's not as what i thought.

how about quasi-linear PDE for this?

Look forward to your help...