ot ll1) r/l1i~u (X) f (Gf) Fev) f:-;~ (v:v) 1 lý) æ (v / find bt(xi (t-i; i/r-(~ v) ta.jpj -- (J ~ Cf, = 0 1l 3 ( J) : o-'t5 : - q 1- eft-1

Μέγεθος: px

Εμφάνιση ξεκινά από τη σελίδα:

Download "ot ll1) r/l1i~u (X) f (Gf) Fev) f:-;~ (v:v) 1 lý) æ (v / find bt(xi (t-i; i/r-(~ v) ta.jpj -- (J ~ Cf, = 0 1l 3 ( J) : o-'t5 : - q 1- eft-1"

Αελλαι Κανακάρης-Ρούφος
6 χρόνια πριν
Προβολές:

1 - la /:_ )( -( = Y () :: ÚlJl:: ot ll) r/li~u (X) f (Gf) Fev) f:-;~ (v:v) lý) æ (v / find bt(i (t-i; i/r-(~ v) bj Ll, :: Qy -+ 4",)( + 3' r.) '.J ta.jpj -- (J ~ Cf, = l 3 ( J) : o-'t5 : - q - eft- F ~)ç2..' r( ui - ( fi.,ùi:i~ 4~ -" 2 'lj'x _,.. f) i'lt =- 4' '* Ljq.rl,X,.' 'X''' I J 2 J '3'.-q? ) '.)o -'.. ~ ft..( l(:l.. -l.4;?t/x-; -~!f'ó.2.3,! - (. ;:i3 _J lo/)\i.. 2. "2'- J.. -/l- +?.q.,.)" ~ tf~ + CtJ ) -- d /L - X'.. i:-:l.cd q J / v ~.- ((,J. i -4 '2 4: -ß (3-) 4 ~"- ~ -.f L /\,- is + C, -; - - b'.. 2 Íf (): =; L2 -.() U\\) -: o::ì ci ;-tf

2 7 "\,\\/exq c r '\ \ \ q tjpto ô C) v~ la3 ~ I '2 ---_._._--_.,- - ai,. aj' X') -: tt 2,)(:- qi X J tl (U~ VI) -= l~. VJ q~. -2q '2-+ i- 4'2 :: ~ 22'2 i L l.5:. I"L.,, 3., 4,.. I 2 ct - n (&I") -.. \ - -" / - I fà '\,, --/L; ) Lt3 ~ /'*X-:l''(L=jQ/te q5 Rit-z V - q - ~ - VL:i -- -,.., -/ VI.. -.j' /id.. - I. I -...'.,

3 J f-lf /I(f i í.. ( la -f V\ - V(tJ :: Cf, Sitff X V/:. ctltf (5 TìX. V - ii - V( -Il "l n l' 7()\. V"':: - tl.,)í3 CISX V IIf -- tiii'síffx #- f~j Ufo) :: tlq) :: la'l-: I. to):: U ///~ V -t U f V :: f f V ) u/l~ V + çti.v -: f tv k,ti;rl U/I/ lj~') la / V I i (t v) ~- (fj V J ) tn f ll I b-. pgj ( I' '6 (.-. ) o - r~. vtl- ) uy') j~, \/F (f) v) (i,ft) -+ (U, v) -:(!. V I.. TT J..V - lí~ U\ V) +lll) It):: Lt/) 4: (4) V) ::C~ v) iyl S t r t 4": V LA - 4. (TT VI i - it6i"'+ n 5 tl l\

4 restart; u d a$sin Pi$ A d 4 Pi$ π 4 C u := a sin π A := 4 π π 4 C de d diff u, $4 Cu =: bca d u =:bcb d DDu =: bcc d u =:bcd d DDu =: s2 d dsolve de, bca, bcb, bcc, bcd, u : plot A$sin Pi$, rhs s2, =.. ; () (2) P3 a) restart; N d 3:h d N : f d 2 $3

5 f := 2 3 de dkdiff u, $2 = f : bca d u =:bcb d u =: ue d dsolve de, bca, bcb, u : for i from to N C do i d i K $h od: p d piecewise % % 2, K 2 K 2, : for i from 2 to N do p i d piecewise i K %! i, K ic % ic,, od: ik ic pnc d piecewise N % % NC, K N NC K N plot p inde $inde =..NC, =.. NC ; K ik ik ik, :, i % (3) uh d sum u n $p n, n =..N C : duhd d diff uh, : for i from to N C do v i d pi od: for i from to N C do dvd i d diff v i, od:

6 eq d u =: for i from 2 to N do eq i d int duhd$dvd i, = ik.. ic = int f$v i, = i K.. ic od: eq N C d unc =: for i from to N C do eq i od: sol d solve eq inde $inde =..NC, u inde $inde =..NC : evalf sol ; u =., u 2 = , u 3 = , u 4 =. assign % ; plot uh, rhs ue, =.. ; (4) b) e d uh Krhs ue : Ee d 2 $int diff e, Ee := Ene := , =.. ; Ene d evalf sqrt Ee ; (5)

7 restart; d :2 d 4 : 3 d 2 : 4 d 3 4 : 5 d :f d 2$3 : p d piecewise % % 3, p2 d piecewise % % 3, p3 d piecewise % % 3, : K3 $ K2 K3 $ K2, : K $ K3 2 K $ 2 K3, : K $ K2 3 K $ 3 K2, 3 % % 5, K5 $ K4 3 K5 $ 3 K4, p4 d piecewise 3 % % 5, K3 $ K5 4 K3 $ 4 K5, : p5 d piecewise 3 % % 5, K3 $ K4 5 K3 $ 5 K4, : plot p, p2, p3, p4, p5, =.. ; uh d u$p Cu2$p2 Cu3$p3 Cu4$p4 Cu5$p5 : duhd d diff uh, : v2 d p2 : v3 d p3 : v4 d p4 : dv2d d diff v2, : dv3d d diff v3, : dv4d d diff v4, :

8 eq d u =: eq2 d int duhd$dv2d, =..3 = int f$v2, =..3 : eq3 d int duhd$dv3d, =..5 = int f$v3, =..5 : eq4 d int duhd$dv4d, = 3..5 = int f$v4, = 3..5 : eq5 d u5 =: s d solve eq, eq2, eq3, eq4, eq5, u, u2, u3, u4, u5 : assign % ; ue d K 5 : plot uh, ue, =..5 ; P4 a e d uh Kue : Ee d 2 $int diff e, 2, =..5 ; Ene d evalf sqrt Ee ; Ee := Ene := restart; N d 2:h d N : f d 2 (6)

9 f := 2 de dkdiff u, $2 = f : bca d D u =:bcb d u =: ue d dsolve de, bca, bcb, u : for i from to N C do i d i K $h od: K 2 p d piecewise % % 2,, : K 2 for i from 2 to N do p i d piecewise i K %! i, K ic % ic,, od: ik ic pnc d piecewise N % % NC, K N NC K N plot p inde $inde =..NC, =.. NC ; K ik ik ik, :, i % (7) uh d sum u n $p n, n =..N C : duhd d diff uh, : for i from to N C do v i d pi od: for i from to N C do dvd i d diff v i, od:

10 eq d int duhd$dvd, =.. 2 = int f$v, =.. 2 : for i from 2 to N do eq i d int duhd$dvd i, = ik.. ic = int f$v i, = i K.. ic od: eq N C d unc =: for i from to N C do eq i od: sol d solve eq inde $inde =..NC, u inde $inde =..NC : evalf sol ; u =., u 2 = 75., u 3 =. assign % ; plot uh, rhs ue, =.. ; (8) b e d uh Krhs ue : Ene d evalf sqrt 2 $int diff e, 2, =.. ; Ene := restart; (9)

11 d :2 d 2 : 3 d : f d 2 : p d piecewise % % 3, p2 d piecewise % % 3, p3 d piecewise % % 3, plot p, p3, p2, =..3 ; K3 $ K2 K3 $ K2, : K $ K3 2 K $ 2 K3, : K $ K2 3 K $ 3 K2, : uh d u$p Cu2$p2 Cu3$p3 : duhd d diff uh, : v d p : dvd d diff v, : v2 d p2 : v3 d p3 : dv2d d diff v2, : dv3d d diff v3, : eq d int duhd$dvd, =..3 = int f$v, =..3 : eq2 d int duhd$dv2d, =..3 = int f$v2, =..3 : eq3 d u3 =: s d solve eq, eq2, eq3, u, u2, u3 ;

12 s := u =, u2 = 75, u3 = assign % ; ue d K$ 2 : plot uh, ue, =..3 ; () e d uh Kue : Ee d 2 $int diff e, 2, =..3 ; Ene d evalf sqrt Ee ; Ee := Ene :=. () P5 restart; N d 2:h d N : f d f := de dkdiff u, $2 C$ diff u, =f:bcad u =:bcb d u =: ue d dsolve de, bca, bcb, u : for i from to N C do i d i K $h od: (2)

13 K 2 p d piecewise % % 2,, : K 2 for i from 2 to N do pi d piecewise i K %! i, K ic % ic,, od: ik ic pnc d piecewise N % % NC, K N NC K N plot p inde $inde =..NC, =.. NC ; K ik ik ik, :, i % uh d sum u n $p n, n =..N C ; 2 % and! 2 uh := u K2 % and % 2 otherwise Cu 2 2 K2 2 % and % otherwise Cu 3 (3)

14 K C2 2 % and % otherwise duhd d diff uh, : for i from to N C do vi d pi od: for i from to N C do dvd i d diff v i, od: eq d u =: for i from 2 to N do eq i d int duhd$dvd i, = ik.. ic C $ int duhd $v i, = ik.. ic = int f$v i, = ik.. ic od; eq 2 := K7 u C4 u 2 C3 u 3 =5 eq N C d unc =: for i from to N C do eq i od: sol d solve eq inde $inde =..NC, u inde $inde =..NC ; sol := u =,u 2 = 5 4, u 3 = (4) (5) evalf sol ; u =., u 2 =.25, u 3 =. assign % ; plot uh, rhs ue, =.. ; (6)

15 e d uh Krhs ue : Ene d evalf sqrt 2 $int diff e, 2, =.. ; Ene := restart; f d f := de dkdiff u, $2 C$ diff u, =f:bcad u =:bcb d u =: ue d dsolve de, bca, bcb, u : d :2 d 2 : 3 d 3 := p d piecewise % % 3, p2 d piecewise % % 3, K3 $ K2 K3 $ K2, : K $ K3 2 K $ 2 K3, : (7) (8) (9)

16 p3 d piecewise % % 3, plot p, p3, p2, =..3 ; K $ K2 3 K $ 3 K2, : uh d u$p Cu2$p2 Cu3$p3 : duhd d diff uh, : v d p : dvd d diff v, : v2 d p2 : v3 d p3 : dv2d d diff v2, : dv3d d diff v3, : eq d u =: eq2 d int duhd$dv2d, =..3 C$ int duhd$v2, =..3 = int f$v2, =..3 ; eq2 := K 28 3 u C 6 3 u2 C4 u3 = 2 3 (2) eq3 d u3 =: s d solve eq, eq2, eq3, u, u2, u3 ; s := u =,u2 = 5, u3 = 4 (2) assign % ;

17 plot uh, rhs ue, =.. ; e d uh Krhs ue : Ene d evalf sqrt 2 $int diff e, 2, =.. ; Ene := (22)

Σχετικά έγγραφα

Q π (/) ^ ^ ^ Η φ. <f) c>o. ^ ο. ö ê ω Q. Ο. o 'c. _o _) o U 03. ,,, ω ^ ^ -g'^ ο 0) f ο. Ε. ιη ο Φ. ο 0) κ. ο 03.,Ο. g 2< οο"" ο φ.

Q π (/) ^ ^ ^ Η φ. <f) c>o. ^ ο. ö ê ω Q. Ο. o 'c. _o _) o U 03. ,,, ω ^ ^ -g'^ ο 0) f ο. Ε. ιη ο Φ. ο 0) κ. ο 03.,Ο. g 2< οο ο φ. II 4»» «i p û»7'' s V -Ζ G -7 y 1 X s? ' (/) Ζ L. - =! i- Ζ ) Η f) " i L. Û - 1 1 Ι û ( - " - ' t - ' t/î " ι-8. Ι -. : wî ' j 1 Τ J en " il-' - - ö ê., t= ' -; '9 ',,, ) Τ '.,/,. - ϊζ L - (- - s.1 ai