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TRUONG DAI HQC TONG HOP HA NOl Khoa Toan - Co - Tin hoc " ' • • ' ' ' ' ^ \ ' DAO HAM TRÜNG BÍNH VA CÁC PHÜONG PHÁP PHOI HCÍP • • DE GIÁI MĨT SO BÁI TOAN BIEN Chuyén ngánh: Toan hoc tính toan Más6 1-01-07 LUÁN AN PHO TIEN SI TOAN LY •^•'^ irifí !\¡Ü>^^, : THAY HUONG DAN: PHÁN VAN HAP MUC LUC Chijdng : M¿ dáu $1 Dao hám trxmE binh tích phan $2- Mót so khái niém bo trO 2.1 Nghiém xáp xi 2.2 Phiidng pháp can bang sai so 2.3 Các phép bien doi toan t\l g ¿: Cae bal toan bien co nghiem khong trun w 6 12 $1_ Bái toan bien d^ng phúc tap có nghiém gián cJoan 12 $2- Bái toan bien dang phúc ta.p có nghiém khóng trdn 17 $3 Bái toan bien dang don gian có nghiém khóng trdn 19 OJlUOn^ ü - Cae bai toan bien co he so khong tron 20 $1 Bái toan bien mot chiéu d^ng don gian 20 $2_ Bái toan bien 26 mot chiéu dang tóng qt ChllĨn^ 4' Cae bai toan bien eo bien ky di 30 $1 Bái toan bien vói phuong trinh laplaxd 30 $2 Bái toan bien vói phildng trinh poatxóng 42 ChliĨnS dMot so philong phap phoi hop giai Bái toan bien khóng dúng tren mién có bien ky di 46 $1- PhUdng pháp bien doi Laplaxd 46 $2 Phildng pháp 50 dng thang $3- PhUdng pháp láp tích phán Phu luC 52 64 - A^ CHÜQNGl MO DAU Trong ehudng md dáu, tac giá trinh báy khái niém deo hám trung binh tích phán, mgt so tính chát quan trgng cüa vá mgt vái khái niém bó trd can thiét cho viéc nghién cúu d chiidng sau $1 Bao hám trung binh tích phán: 1.1 Sinh nghia [13]: i) Xét F:X —••• Y (X,Y - B khóng gian)' , Xo ^ X néu V h "íi X , ton tîi: ( lim S-i-O F(xo+th)-F(xo) dt - SFCxo,h) 2Í /g- t thif F(xo,h) ggi bien phán trung binh (theo thú cüa hám F tai xo tích phán) iij Néu tai Xo ta cc5'F(xo,h) ~ Ah dó A - Toan tü tuyen tính giói ngi, thi F dUdc ggi la vi trung binh, co dao ham trung binh theo tích phán t§.i Xo, vá viét F'(xo, h)= Ah Nhán xét: De muc dinh nghién cúu cüa luán án nén ó dáy chi sü dung d&o ham trung binh tích phán theo dinh nghia tren Ta có thé md róng dinh nghia tren báng cách thay thé biéu thúc tronfe i) bói biéu thúc: F(xo+th)-F(xo) 1 im ^-••0 Ĩ dáy: dt = ĐF(xo.h) (ô+P )S -ai ô, B > O 1.2 Tinh chát [13] i) Hién nhién ta có: (FTG)( lim ^'-Ô f(t)dt = 2ó im [f(5) - f(-Q)] S-^0 -5 F(Xo-i-5h) - F (Xo) F (Xo-5h) F(xo+§h) - F(xo) — lim — 5^ L^-Ô F'(XO-HO) F(xo-5h) - F(xo) -í + lim + F'(xo-O) ==> (dfcm) $2 Mót s6 Jdiái niém b6 tro 2-1- Nghiém xáp xi [1] iriá sü can tim nghiém :i + «o 1=1 ' (2.1.4) ó dáy ai(i=0,n) só can tim; { *íî(x) } (1=1,=^ ) hám dáy dü, túc thoa man dieu kién sau: i) { ¥'i(x) }._ dóc láp tun tính V n ii) V£> O, Vu,3n cho: Dat (2.1.4) [u- (ZtXiíí?i-HXo)] d x váo (2.1.1), ^ (2.1.2), i ¿ (2.1.3) ta R: = L ( U * ) - b TÍ O (2.1.6) Ri: = S(ü*) (2.1.7) Rs: = - s ?í O G(U") - g / O ¿xiOc: (2-1.8) Trong viee tim nghiem xap xi U cho ham sai se R, Ri, Ra dude xác dinh bdi (2.1.6), (2.1.7), (2.1.8) có giá tri bé túy y tren Q + r, da xuát hién nhieu phucng pháp ly thú Dé phuc vu cho viéc nghién cúu d chüdng sau, chúng tói trích dan phiidng pháp can báng sai só dUdc trinh báy [1] 2-2- PhUdng pháp can bang sai so Giá thiét rang VW déu viét dUde duói dang: Z Bifi i=l "trong dó {^î} Thé thi moi ham (2.2.2- la hám dáy du ; {3 i} u thoa man dieu kién so bien ~inh dúngtúc lá: Ri = Rs - O j (2.2.2) 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 va: (R,W) = (2.2.3) R.Wdo = O ¿\ióc g o l l nghiém x p x i c ü a b i t o a n ( ) , ( ) ; W dUdc g o l l hám t r o n g lUdng Dinh l y ( G a u x d - O s t r ó g r a t x k i ) Míen ii Büóc gla thlet^npl va Bón lien, quy, thé thi: f"^' mat f' la kin va chinh 3w 3u (w 'v^ u - u ^ " w ) dQ (2.1.2), (w -) u an ds (2.2.4) Bao hám ^n Q 3u Trong 36 V toan tü Laplaxó ; 3w ^ ^ _ an theo pháp tuyen 3n cua cae hám u^ w túóng úng 2-3- phép bién doi toan tU: 2.3.1 Phép bién doi LapIaxO mót chiéu: i) Dinh nghia: Phép bien Bol Laplaxó mot chleu phép 361 Bat túóng úng mol hám f(t) mot hám F(s) Búóc xác Binh Báng thúc: F(s): = ^ C f ( t ) , s] bien bol f(t) e ^"^ dt ii) Dieu kién dü dé ton tai phép bién dói Laplaxd mgt chiéu: Phép bién dói Laplaxd mót theo nghia hgi tu tuyét dói néu: chiéu cua hám + 0O a) Ton tai J if(t)[e f(t)(e o b) Ton tai ^ [f(t), s] dt 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 f(t) ton tai 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 - iii) Phép bién dói ngUdc Laplaxd mót chiéu: Phép bién dói dat tUdng úng moi hám^F(s) mgt hám f(t) má y [f(t),s] = F(s) dude ggi phép bién dói ngUOc Laplaxd mgt chiéu cüa hám f(t); vá viét; f(t) = ^ "^[F(s)] iv) S\t ton tai cüa phép bién dói ngU0c Laplaxd a) Néu F(S) hám tai^^[F(s)] giái tích vá có cap nhó non (-1) thi ton b) Giá sü F(s) ' ^[Fi(s), F,2(s), , , Fn(s)] Trong dó ^(zi, zs, -., Zn) hám thoa man dieu kién: '^(Z1,Z2, , Z n ) ~ O < = => Zl = Z2 - Fic(s) = ¿' [fi^(t),s] thi ot CF(s)] ton tai hgi tu tuyét dói = Zn = O ; Vk = l,n vá phép bién dói Laplaiíd tUdng úng v) Tính chát cua phép bién dói Laplaxd: a) Gia thiét Fi(s), F2(s) bién dói Laplaxd cüa hám fi(t), f2(t) tUdng úng Thé thi V «, B ik háng so ta có; [ocfi(t) + tif2(t),s] = ocFi(s) + BF2(S) ^ b) Gia thiét F(s) phép bién dói Laplaxd cüa hám f(t), vá ton tai f (t) Vt > O dó: ^ [f'(t),s] = sF(s) - f(0+0) c) Gia thiét F(s) phép bién dói Laplaxd cüa tai dao hám cap r cüa hám f(t) Vt > O the thi; ^ ífit), s] = s F(s) - s f(0+0) - f f(t) vá ton (0+0) d) Neu^f(ü) hám giói ngi Vt >0 vá ton tai f'(t) Vt>0 "crú diém t=ti, ta, má tai dó f''t) có cae giói han hai phía húu han, thi ^ [f'Ct),s] = 3F(o)-F(0+0)-Zexp(-t±s) [f(ti+O )-x(-i-O ) ] e) Giá sü F(s) phép bién doi vói moi háng só a ta có: Laplaxd cüa hám f(t) dó 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 - 10 %í [f(a.t),s] = a F( ) f) Giá thiet F(s,íx) phép bién dói Laplaxd cüa hám f(t,'-x) dó « tham so khóng phu thuge váo t vá s Thé thi: ^[lim f(t,'o(),s] - lim F(s,ü() üt—*-a ot—*-a g) Giá thiét F{s) phép bién dói Laplaxd cua f ( t ) , dáng thúc sau: ta có + S^^t t f(t),s|= F'(s) + oC L^~^^ ^ x(t)^Sj= F (s) 4-m 5r[t~^ fft)^^= F^(s)ds (Néu tích phán hgi t u ) Tú tính chát b, vá d, ta có dinh ly thiét láp mói quan cüa phép bién dói Laplaxó vá dao hám trung binh nhu sau: trung f(t): Gla thiét f(t) glól nól Vt>0, binh f'(t) Vt>0; F(s) phép bien ton tal Bao hám Bol Laplaxó cua + Néu f(t) lien tuc thi-ta có: 3^ [ f - t ) , s] = sF(s) - f(0+0) + Neu f(t) có giói han hai phía hüu han tai tx, t2 thi Ífcf'(t), 3] = iF(s) - f(0+0)- i:exp(-tiS) [ f(ti+0)-f(ti-0) j V 2.3.2 Phep bién dói T.FJPlaxd hai chiéu: Phép bién dói Laplaxd hai chiéu phép bién i) Dinh nghia: dói dat tUdng ung moi ham í.\x.) mgt ham Fís) co dang: 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 11 x^[f(t) F(s) = =oCo[f(t),s)] = f(t)e ^ dt ii) Quan giüa bién dói Laplaxd hai chiéu vá mgt chiéu: Giá thiét ton tai phép bién dói Laplaxd vá hai chiéu cho hám f(t) thé thi: mgt chiéu ^ [ f ( t ) , s ] = ^[f(t),s] + ^[f(-t),s] iii) Tính chát cüa phép bién dói Laplaxd hai chiéu: Nhiéu tính chát cüa phép bién dói Laplaxd hai chiéu ¿xií^c suy tú tính chát cüa phép bién dói Laplaxd mgt chiéu Trong trng hOp riéng ta có; a) ^B'[f(t),s] = ^ [f(t),s] /? néu f(t) = O t ^ c a) ¿ f s [f(t),s] - ^[f(t),s] ^ neu f(t)=0 t i c 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 - 61 tf ¿ G i j (0) = (P(l) Vdi: p(x) = , q(x) , f(x) = X vi du náy dUde giai báng lude sai phán chudng 3, vá phUdng pháp Gaioekin tren máy tinh dién tú, ket cho dó chinh xác nhU NhUng ta tháy lUdc sai phán chUdng ddn gian hdn nhiéu VI du Xét bái toán ; ^ ^ u ^ O X ^- (0,1) X «e r 3u u 3n Vi du dude giái báng phUdng pháp trinh báy chUdng cho truóng hdP a = 1,2,3, tren máy tinh dién tu Ket tinh toán düdc so sánh vói nghiém dúng cua oai toan vá cho dó chinh xác cao 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 - ^ p e : V e L t, t> !• ••-••,-, !'• 1- a y f |_ „ n I ] D f bs- T ¿O ; i'ar n , i , j !.: i n I eyer-; ín s | : : a r r r t > [ - , n J n f r eaJ.; { ' 1- ií\ ) ' , A , Í; ; i f n: • n :i 111 '.< o vi v i t e 111 ( ' A11 o w o 111 yn i , ' no I íB l o p s ' ) un t'j t rirocéd u r e f i v r r su /l'l a I r i x ( v a r A ^ B ^ C s '.-e c; t o r ) ; Vc-ir ÍI,V2Vi?r.: l o r ; |)eqin O n a k e U ( l ) - U C n ) > ULÍ]:-1;;ÜL2.1: — ( A L : I / B L : I ) ; Por i : - t o n - d o UL i : : i : - • • ( (CL i - : ) t t l L i 2:i t AL i - l J ^ M I L i - J ) / í ^ L i - I J ) I I L , n - J : - / ( C L n • ] t U L11 " J i A L r^ - ] ^1^ U I n • j ) ^ {make R m a t r i x ] f o r i : - t o n - d o F:L l n - :i í - Ü L i il^l^l^lL , i' i 1;; RLÍ,n-tJ:-HLl,n-i::i; m : l n - : ! : - ( R t K r - i : i : i ' A L n :iM:iLn- : i ) ; f o r i í - n ' - d o w n U ) d o RL , i : - • ( (RL i ' I t C L i r r ] H^^f ; i H |:í.AL i ' H ) / r ( L i I ) ; f o r- j ;"" I o n - d o •for •feI i:=^^2 l o i : •••2 t o j d o RL :i , J ] " = 1J[ J'f-RL U J ü ; n ~ l ror i::^^l t o i - RLi , jJr^Ô; 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0-003; I -L22:i>'L2AJ-^: 'rtop 023:; 0-OOü: yL23;:k:'L2/J^- 0»01?; o.oo:'.í DI 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 -¿gC CHUONG TRINH GIAI HE PT BAC NHAT AN SO DIMENSIÓN A ( , ) , U ( ) , G ( , ) , D ( ) , B ( ) , X(4) CHAnACTER*80 TENMATRAN CHARACTER*80 Tl,T2,T3 N = KR = KW = C DOC CAC MA TRAN A, G, I) TU TEP HESO.DAT OPEN(KR, FILE=*HES01.DAT') READ(KR,*(A)') TENMATRAN W R I T E ( * , * ) TENMATRAN DO I = , N READ(KR,*) (A(T,J),J=1.N) CONTINUÉ READ(KR, M A ) ' ) TENMATRAN DO 21 I=1,N READÍKR,*) (G(I,J) ,J=] ,N) CONTINUÉ 21 C C C MO TEP HEPT.KQ DE IN KET QUA OPENÍKW, FTLE='HEPT.KQJ *, STATUS = MJNKNOWN*) Tl=' —— ' T2=* DIEM SO I NGHIEM THEO D H T BINH I NGHIEM GIAI TICH I ' T3=* 6000 FORMATÍTl , ' | M T ' | \ F15 T32 , * | ' ,F15.3,T50, ' I ' ) WRITEÍKW, '(lOX.A//) ' ) ' KET QUA GIAI HE PHUONG TRINH TUYEN TINH' WRITE(KW,*) 5100 C C C WRITE(KW M A ) ' ) ' MA TRAN G' DO 5100 I =1,N WRITE(KW,501) (G(I,J) J=1.N) CONTINUÉ WRITE(KW,*) WRITEÍKW, M A ) M TI WR]TE(KW, M A ) ' ) T2 WRITE(KW, M A ) M T3 TINH CHO TUNG TRUONG HOP ' DO 1000 K=l,3 DOC NGHIEM GIAI TICH READ(KR M A ) * ) TENMATRAN READÍKR.*) (D(I),1=1,N) C READ(KR M A ) ' ) TENMATRAN READÍKR,*) (X(I).1=1,N) 111 READÍKR.MA)') TENMATRAN DO 111 1=1,N READÍKR,*) (Ai I,J) ,J=l ,N) CONTINUÉ 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37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 -?0 CALL NHANÍG.D.B.N) C 133 C 501 500 WRITEÍKW,1333) K FORMATÍ * TRUONG HOP THU Ml3) WRITEÍKW, M A ) *) * MA TRAN HE SO* FORMATÍ4F15.3) DO 500 I =1,N WRITEÍKW,501) (AÍT,J), J=1,N) CONTINUÉ WRITEÍKW.MA)*)' MA TRAN B ' WRITEÍKW.501) (B(I).1=1.N) WRITEÍKW M A ) •) ' MA TRAN D * WRITKW,501) ÍD(I),1=1,N) C CALL NxNÍA,U,B.N) PAUSE C IN KET QUA DO 1992 = ,N WRITEÍKW,6000) I,U(I).XÍI) 992 CONTINUÉ 000 CONTINUÉ CLOSEÍKR) CLOSE(KW) STOP END C CHUONG TRINH NHAN HAI MA TRAN SUBROUTINE NHANÍG.D.B.N) DIMENSIĨN GÍN.N), DÍN) B(N) DO 100 I = 1, N B(I) = O DO 101 J = N BÍI) = BíI) + Gil,J)*DÍJ) WRIT* MF10.2) * ) BÍI) 101 CONTINUÉ 100 CONTINUÉ END C C C CHUONG TRINH GIAI HE PHUONG TRINH TUYEN TINH SUBROUTINE NxN(A.X.B,N) DIMENSIĨN A(4,4).XÍ4),B(4) All A12 AIN I Bl c c C ANl AN2 ANN | BN DO 100 IHANG =1.N C TGIAN=IHANG.IHANG) BíIHANG)=BÍIHANG)/TGIAN DO 333 J=l,N A íIHANG.J)=A íIHANG,J)/TGIAN CONTINUÉ 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 333 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37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 1^^ KET QUA GIAI HE PHUONG TRINH TUYJRN^TlNjí TRAN HE SO 2.150 035 -2.079 035 035 2.150 035 -2.079 -2.079 305 2.150 035 035 -2.079 035 2.150 150 2.610 150 -2.770 -2.770 150 2.610 150 150 -2,770 150 2.610 1.000 1.000 \ TRAN G 2.610 150 -2.770 150 TRUONG HOP THU MA TRAN D 1.000 000 DIEM SO NGHIEM THEO D H T BINH NGHIEM GIAI TICH 000 2.000 000 2.000 -.006 989 -.006 1.989 TRUONG HOP THU MA TRAN D 2.000 2.000 2.000 DIEM SO NGHIEM THEO D H T BINH NGHIEM GIAI TICH 0.978 3.008 0.978 3.008 000 3.000 1.000 3.000 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 2.000 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37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.99 3.000 37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.2237.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.66 ^ - 74 TAI LIEU TEM KHAO /"I_7 EpeóóHH K, Tejuiec H , Bpoydeji Merojiti rpaHatiHHx sjteMeHTOB '^ííocKsa" 1987 Z"2_7 rojQTHOB C.K., pfíóeHBKHđ H.íí., pasHOCTHHe cxe™ "HayKa" M.I972 /"3_/ Map^K r H , MaTeMaTH^cKoe.MOBejijapoBaHEie B npoóJieMe OKpyxameft cpejis ^'HayKa" M.I982 /*4_7 iVÍap^K r K MeT^ BH^CJiHTejTBHOfí MaTeMaT2K2 "HayKa", HOBOCHĨRípCK 1973 /"5_7 lanEiseHCKaH O.A,, KpaejBHe s a j í a s ífeteMaTü^cKoS ^nsKKii, '"Hayxa", M., 1973 ¿"5_7 JlKiiiKO H.ií., BewT;iKOírBaHHEKO II.M napHK B,I!., 'JacrenKHS r S , MeTo;i MaxopaHTHHx Jiacri B TGOPÍÜB lajiBTpaiiM "HayKCBa ;iyMKa^ Kaes 1974 /"7_7 CaiviapcKafi A.A TeopHH pasHOCTHHx cxeM M.I977 /"8_7 HEGHKO L^J Manolis G.D, and Beslcos D.E , Dynamic s t r e s s comcentret i o a atudies by boucdary i a t e g r a l s and laplace transf o m , I n t J.Numerical r.!ethod 1981 H.H,, MeTOfl apoóHHx maroB penreHH£ MHoroMepHHi aasaq MaTeuaTJaqecKOfi áiHsaKE, "HayKa" SocoMíapcK, 1967 /"10 Le Dinh Binh An a p p l i c a t i o n of average deriyetives i n sorae Boundar:;" - valué pir^blems, the congresa of Vietnamese methemeticiaos Eeooi, September 4-7, 1990 ( A b s t r a c t s ) /~11^7 Le Dicii Dioh, An e p p l i c a t i o a of average derivatives i n compártemental raodels S c i e n t i f i c confereace, Paculty of Mathematics, Mechanics and informática 5tate Uoivers i t y , Nov, 1991 ( A b s t r a c t s ) 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