- #1

ShayanJ

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## Main Question or Discussion Point

One of my friends needs to numerically solve this two dimensional boundary value problem but has now idea where to begin. Could anybody help?

## [(K H )(f g_x-gf_x)]_x+[(K H )(f g_y-gf_y)]_y=0 ##

## K H G^2 (f^2+g^2)+\frac 1 2 [KH (f^2+g^2)_x]_x+\frac 1 2 [K H (f^2+g^2)_y]_y-K H[((f_x)^2+(g_x)^2)+((f_y)^2+(g_y)^2)]=0##

Where K,H and G are known functions of x and y and the unknown functions are f and g.

The boundary conditions are:

## f_x=- G \beta g ## and ## g_x=G\beta f ## at x=0.

## f_x=G g ## and ## g_x=G(2A-f) ## (A=const) at ##x\to \infty ##.

## f_y=g_y=0 ## for both ## y\to \pm \infty ##.

Is there any hope?

## [(K H )(f g_x-gf_x)]_x+[(K H )(f g_y-gf_y)]_y=0 ##

## K H G^2 (f^2+g^2)+\frac 1 2 [KH (f^2+g^2)_x]_x+\frac 1 2 [K H (f^2+g^2)_y]_y-K H[((f_x)^2+(g_x)^2)+((f_y)^2+(g_y)^2)]=0##

Where K,H and G are known functions of x and y and the unknown functions are f and g.

The boundary conditions are:

## f_x=- G \beta g ## and ## g_x=G\beta f ## at x=0.

## f_x=G g ## and ## g_x=G(2A-f) ## (A=const) at ##x\to \infty ##.

## f_y=g_y=0 ## for both ## y\to \pm \infty ##.

Is there any hope?