_WELCOMETO Radioland

Top50  











.




.








.














> >

: 3/4

 

1) =0 ( G)

U = 0

x=o

Uxxx = 0

x=o

 

 

Uoj=0

U-1j=U2j - 3U1j (1`)

 

 

2) =ࠠ ( G)

i=N

 

Ux = 0

x=a

Uxxx = 0

x=a  Ui+1j - Ui-1j = 0

2hx

 

UN+1j = UN-1j

UNj = 4 UN-1j - UN-2j (2`)

3

 

3) =0 ( G)

j=0

 

Ui ,-1 = Ui1

Ui0 = 0 (3`)

 

Uy = 0

y=o

U =0

y=o

 

4) =b

i=M

 

U = 0

y=b .. UiM=0 (**)

 

Uxx + Uyy =0 j=M (**)

 

UiM-1 = UiM+1

 

=b

 

UiM+1 = UiM-1

UiM = 0 (4`)

 

(*) W (1`)-(4`) G ( W)

 

 

 

(*),(1`) - (4`).

 

Uij = U(xi,yj)

xi = ihx

yj = jhy

hx = a/N ,

hy = b/M

x , N [0 , ] [0 , b]

 

2

DU = f

 

. W , .

 

1 Ui-2j - 4 + 4 Ui-1j + 6 - 8 + 6 Uij - 4 + 4 Ui+1j + 1 Ui+2j + 2Ui-1j-1 -

4 4 2 2 4 2 2 4 4 2 2 4 2 2

hx hx hxhy hx hxhy hy hx hxhy hx hxhy

 

 

- 4 + 4 Uij-1 + 2 Ui+1j-1 + 2 Ui-1j+1 - 4 + 4 Uij+1 + 2 Ui+1j+1 + 1 Uij-2 +

2 2 4 2 2 2 2 2 2 4 2 2 4

hxhy hy hxhy hxhy hxhy hy hxhy hy

 

 

+ 1 Uij+2 = f ij i=1 ... N-1, j=1 ... M-1

4

hy

U (1`) - (4`), 13 13- . :

(k+1) (k+1) (k+1) (k+1)

6 - 8 + 6 Uij = - 1 Uij-2 - 2 Ui-1j-1 + 4 + 4 Uij-1 -

4 2 2 4 4 2 2 2 2 4

hx hxhy hy hy hxhy hxhy hy

 

 

(k+1) (k+1) (k+1) (k)

- 2 Ui+1j-1 - 1 Ui-1j + 4 + 4 Ui-1j + 4 + 4 Ui+1j -

2 2 4 4 2 2 4 2 2

hxhy hx hx hxhy hx hxhy

 

(k) (k) (k) (k) (k)

- 1 Ui+2j - 2 Ui-1j+1 + 4 + 4 Uij+1 - 2 Ui+1j+1 - 1 Uij+2 + fij

4 2 2 2 2 4 2 2 4

hx hxhy hxhy hy hxhy hy

 

(k)

U (1`) - (4`). i=1, j=1 W. n = (N-1)(M-1).

.. 13 ( ) - .