12 2006
12 2006
12 2006
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TÜRKMENISTANDA YLYM WE TEHNIKA<br />
НАУКА И ТЕХНИКА В ТУРКМЕНИСТАНЕ<br />
SCIENCE AND TECHNICS IN TURKMENISTAN<br />
№<strong>12</strong> <strong>2006</strong><br />
G.Judakowa<br />
GILBERT GIŇIŞLIGINDE GIPERBOLA-ELLIPTIK DEŇLEMELERI<br />
ÜÇIN IKINJI TERTIPLI TAPAWUT SHEMASY<br />
Giperbola deňlemeleri üçin ikinji tertipli tapawut shemasy we elliptik<br />
deňlemeler üçin ikinji tertipli tapawut shemasynyň gurluşy şu aşakdaky ikinji tertipli<br />
tapawut shemasynyň ýakynlaşan çözüwi üçin gyra meselesine seredilýär [1, 2, 3]:<br />
2<br />
⎧uk+<br />
1 −2uk<br />
+ uk−1<br />
τ 2<br />
⎪<br />
+ Au +<br />
+ = ,<br />
2<br />
k A uk<br />
1<br />
fk<br />
⎪<br />
τ<br />
4<br />
⎪fk<br />
= f ( tk<br />
), tk<br />
= kτ<br />
,1 ≤k<br />
≤ N −1,<br />
Nτ<br />
= 1<br />
⎪<br />
⎪<br />
uk+<br />
1 −2uk<br />
+ uk−<br />
1<br />
−<br />
+ Au = ,<br />
2<br />
k gk<br />
⎨ τ<br />
⎪gk<br />
= g( tk<br />
),<br />
tk<br />
= kτ<br />
, −N<br />
+ 1 ≤k<br />
≤−1,<br />
u0<br />
= ϕ,<br />
⎪<br />
2<br />
⎪<br />
τ<br />
⎪uN<br />
= u−N<br />
, u1<br />
−u0<br />
− 0 0 0 −1<br />
2<br />
⎪<br />
⎩g0<br />
= g(0),<br />
f0<br />
= f (0),<br />
2<br />
τ<br />
2<br />
( f − Au ) = u −u<br />
− ( g − Au )<br />
0<br />
0<br />
(1)<br />
we<br />
⎧uk+<br />
1<br />
−2uk<br />
+ uk<br />
−1<br />
1 1<br />
⎪<br />
+ Au + ( +<br />
2<br />
k<br />
Auk<br />
+ 1 Auk<br />
⎪ τ 2 2<br />
⎪fk<br />
= f ( tk<br />
), tk<br />
= kτ<br />
,1 ≤k<br />
≤ N −1,<br />
Nτ<br />
= 1<br />
⎪<br />
⎪ uk<br />
+ 1<br />
−2uk<br />
+ uk<br />
−1<br />
−<br />
+ Au = ,<br />
2<br />
k<br />
gk<br />
⎪ τ<br />
⎨gk<br />
= g( tk<br />
),<br />
tk<br />
= kτ<br />
, −N<br />
+ 1 ≤k<br />
≤−1,<br />
u0<br />
= ϕ,<br />
⎪<br />
2<br />
2<br />
⎪<br />
I + A τ<br />
uN<br />
= u−N<br />
,( I + )( u1<br />
−u0)<br />
−<br />
0<br />
⎪<br />
4<br />
2<br />
⎪<br />
2<br />
⎪<br />
τ<br />
= u0<br />
−u−<br />
1<br />
− ( g0<br />
− Au0)<br />
⎪ 2<br />
⎪<br />
⎩g0<br />
= g(0),<br />
f0<br />
= f (0),<br />
−1<br />
) =<br />
( f − Au )<br />
0<br />
f<br />
k<br />
,<br />
1-nji teorema. Goý, ϕ ∈D(A)<br />
. Onda (1) differensial shemanyň çözüwi üçin<br />
şu deňsizlikler adalatlydyr:<br />
29