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!!!

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- May 2nd 2008, 04:05 PMWangTaoSGHow 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 PMmr fantastic
- May 3rd 2008, 04:43 AMWangTaoSGIs 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 PMmr fantastic
$\displaystyle \frac{\partial w}{\partial x} \, \frac{\partial w}{\partial y} = F(x, y)$.

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 PMWangTaoSGWill 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...