12 2006

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TÜRKMENISTANDA YLYM WE TEHNIKA НАУКА И ТЕХНИКА В ТУРКМЕНИСТАНЕ SCIENCE AND TECHNICS IN TURKMENISTAN №<strong>12</strong> <strong>2006</strong> G.Judakowa GILBERT GIŇIŞLIGINDE GIPERBOLA-ELLIPTIK DEŇLEMELERI ÜÇIN IKINJI TERTIPLI TAPAWUT SHEMASY Giperbola deňlemeleri üçin ikinji tertipli tapawut shemasy we elliptik deňlemeler üçin ikinji tertipli tapawut shemasynyň gurluşy şu aşakdaky ikinji tertipli tapawut shemasynyň ýakynlaşan çözüwi üçin gyra meselesine seredilýär [1, 2, 3]: 2 ⎧uk+ 1 −2uk + uk−1 τ 2 ⎪ + Au + + = , 2 k A uk 1 fk ⎪ τ 4 ⎪fk = f ( tk ), tk = kτ ,1 ≤k ≤ N −1, Nτ = 1 ⎪ ⎪ uk+ 1 −2uk + uk− 1 − + Au = , 2 k gk ⎨ τ ⎪gk = g( tk ), tk = kτ , −N + 1 ≤k ≤−1, u0 = ϕ, ⎪ 2 ⎪ τ ⎪uN = u−N , u1 −u0 − 0 0 0 −1 2 ⎪ ⎩g0 = g(0), f0 = f (0), 2 τ 2 ( f − Au ) = u −u − ( g − Au ) 0 0 (1) we ⎧uk+ 1 −2uk + uk −1 1 1 ⎪ + Au + ( + 2 k Auk + 1 Auk ⎪ τ 2 2 ⎪fk = f ( tk ), tk = kτ ,1 ≤k ≤ N −1, Nτ = 1 ⎪ ⎪ uk + 1 −2uk + uk −1 − + Au = , 2 k gk ⎪ τ ⎨gk = g( tk ), tk = kτ , −N + 1 ≤k ≤−1, u0 = ϕ, ⎪ 2 2 ⎪ I + A τ uN = u−N ,( I + )( u1 −u0) − 0 ⎪ 4 2 ⎪ 2 ⎪ τ = u0 −u− 1 − ( g0 − Au0) ⎪ 2 ⎪ ⎩g0 = g(0), f0 = f (0), −1 ) = ( f − Au ) 0 f k , 1-nji teorema. Goý, ϕ ∈D(A) . Onda (1) differensial shemanyň çözüwi üçin şu deňsizlikler adalatlydyr: 29
30 H ] k H k H H k f A N k g A k N M u N k N 2 1 2 1 1 0 max 0 1 max max − − − ≤ ≤ + ≤ ≤ + − + ⎢ ⎣ ⎡ ≤ ≤ ≤ − ϕ [ ∑ ∑ ∑ ∑ + =− − = − − − + + =− − = + − − ⎥ ⎦ ⎤ − + − + + + + ≤ ≤ ≤ − + + − − ≤ ≤ + − ⎥ ⎦ ⎤ + + + ⎢ ⎢ ⎣ ⎡ ≤ ≤ ≤ − + − ≤ ≤ + − 0 1 1 1 1 1 0 0 2 1 1 0 1 1 0 2 1 2 1 1 max 2 1 1 max max 1 max N k N k H k k k k H H H H k H k k k N k N k H k H k H H k H k k f f H g g f g A M Au N k N u u u N k N f g A M u A N k N u u N k N ϕ τ τ τ ϕ τ Bu ýerde, M 0 1 , 1, ,0 we , , ≤ ≤ + − − ≤ ≤ k N g N k f k k ϕ τ bagly däl. Teoremanyň subudy şu formulalar esasynda: [ ] [ ] ] [ 2 4 , ) (1 1, 1 ) )(2 ( ) (2 ) ( ) ( ) ( ) ( , ) 2 (1 ) ( 1, 1 , ) ( ) ( 2 ) ))( ( ) ( ( )) ( ) ( ( 2 ) ))( ( ) ( ( )) ( ) ( ( ) ( )) ( ( ) ( 1) ) ( ( )) ( ) ( ( 2 1 1 1 1 1 ) ( 1 1 1 1 1 1 1 2 0 1 2 0 1 2 2 1 2 1 2 1 2 1 2 1 1 1 0 2 1 2 1 1 2 1 2 1 2 1 0 2 1 2 1 1 2 1 2 1 0 2 1 1 2 1 2 1 1 2 1 1 2 1 2 1 2 1 + + = + = ≤ − ≤ + − + − + + − − − + − − − + = − ± = ± − ≤ ≤ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ − − − − − − − − + + − − − − − + − − + − − − − = − − − + =− − − + − − − − + − − + =− − + − − − + − − − − − − − − = − − − − − − ∑ ∑ ∑ A A A B B R k N g R B R R B g B R R R B R R R I u u R R R R I u R u A A i A D N k f A D A D x x A i g f A D A D A D A D u u A D A D A D A D U A D A D I A D A D A D A D u S N S k S S k S S N S N N S k N k N N N N k N k N N k k S S k S k k S o k k k k k k k τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ
Page 2 and 3: TÜRKMENISTANDA YLYM WE TEHNIKA SCI
Page 4 and 5: BEÝIK SERDARYMYZYŇ YLMY NAZARYÝE
Page 6 and 7: Oba hojalyk ylmy boýunça Ylmy-bar
Page 8 and 9: TÜRKMENISTANDA YLYM WE TEHNIKA Н
Page 10 and 11: ýaly, göýä öňki hereketine pu
Page 12 and 13: Б.Басаров К ВОПРОСУ
Page 14 and 15: - Biologik baýlyklardan rejeli pe
Page 16 and 17: Günorta Türkmenistanda oba hojaly
Page 18 and 19: tarapyndan süýşýän çägeleri
Page 20 and 21: TÜRKMENISTANDA YLYM WE TEHNIKA Н
Page 22 and 23: alnan maglumatlaryň seljerilmegi n
Page 24 and 25: 2-nji tablisa Hananyň durnuklylygy
Page 26 and 27: suwuň möcberi 120 m 3 /s bolanda,
Page 28 and 29: Bar bolan barlaglaryň maglumatlary
Page 32 and 33: 31 ] { [ ] } } s S N S N N S k k S
Page 34 and 35: 33 ( ) ⎪⎭ ⎪ ⎬ ⎫ ⎟ ⎟
Page 36 and 37: 35 { ( ) [ ] }+ + − + + − ×
Page 38 and 39: G.Judakova SECOND ORDER DIFFERENCE
Page 40 and 41: Ýokarda görkezilişi ýaly edip,
Page 42 and 43: * * P1 −1 P2 −1 Pn −1 −1 n
Page 44 and 45: 5051+44)=[5051,5095) aralykda iň a
Page 46 and 47: Türkmenistanyň Prezidentiniň ýa
Page 48 and 49: Gorkut aýy - № 7 Durdyýew B.K.,

12 2006

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