x l; =a+j*h; write('x=',xl:5:2);
for i: = l to nurav do write(' yf'.i: 1, ]=',y[i]:10:6);
x O := x l; yO :=y;
writeln;
end;
end.
M isol. B erilgan dastur y o rd am id a, ushbu
iy'i(x) = y, (х ) + У2( х ) + 4 х ~
1
\у \(х ) = у , ( х ) - у г( х ) ~ 2 х 1 - 2 x + \
differensial ten g lam alar tizim ining
b , ( 0 ) = -
1
U r o ; = i
b o sh lan g ‘ich shartlarni q an o atlan tiru v ch i yechim ini aniqlang ( o =
0
,
b =
1
,
« = 1 0
deb
oling).
Y e c h ish . Ishonch hosil
qilish m um kinki, berilgan K oshi m asalasi ushbu
{ y f x ) = x - - x - \
[ У г ( х ) = ~ х 2 - X + l
aniq y e ch im g a ega. M asalan in g an iq v a dastur y o rd am id a to p ilg an taqribiy
yechim lari q u y id ag i ja d v a ld a keltirilgan.
X
У , ( х )
У г ( х )
A n iq
yechim
taq rib iy yechim
aniq yechim
taq rib iy yechim
0 , 0
-
1 . 0 0 0 0 0 0 0 0 0
-
1 . 0 0 0 0 0 0 0 0 0
1 . 0 0 0 0 0 0 0 0 0
1 . 0 0 0 0 0 0 0 0 0
0 ,1
-1.09 0 0 0 0 0 0 0
-1.090000000
0.890000000
0 .889999166
0 , 2
-1 .1 6 0 0 0 0 0 0 0
-1 .1 6 0 0 0 0 0 8 4
0.760000000
0 .759998408
0,3
-
1 . 2 1 0 0 0 0 0 0 0
-1.210000253
0.610000000
0 .609997710
0,4
-1.24 0 0 0 0 0 0 0
-1.240000511
0.440000000
0 .439997058
0,5
-1.25 0 0 0 0 0 0 0
-1 .250000862
0.250000000
0 .249996438
0 , 6
-1 .2 4 0 0 0 0 0 0 0
-1.240001315
0.040000000
0.039995840
0,7
-
1 . 2 1 0 0 0 0 0 0 0
-1.210001 877
-0.190000000
-0.190004750
0 ,8
-1.16 0 0 0 0 0 0 0
-1.160002561
-0.440000000
-0.440005343
0,9
-1 .0 9 0 0 0 0 0 0 0
-1.09 0 0 0 3 3 8 0
-0.710000000
-0 .710005952
1 ,0
-
1 . 0 0 0 0 0 0 0 0 0
-1 .000004350
-
1 . 0 0 0 0 0 0 0 0 0
-1 .000006587
6.5. C h e k li
a y ir m a la r usuli
C hekli ay irm alar usuli d ifferen sial tenglam alarni taqribiy y ech ish usuli
b o ‘lib, u n o m a ’lum funksiya hosilasini chekli ayirm alarga alm ash tirish g a asoslan-
gan. Soddalik uchun bu
usul algoritm ini quyidagi
у ( t ) + A ( t ) y ( t ) + B ( t ) y ( t ) = F ( t )
(6.17)
d ifferensial ten g lam an in g
у ( 0 ) = С 0,
у ( 0 ) =
D„
(6.18)
90
boshlangM ch shartlarni qanoatantiruvchi yechim ini topish m asalasid a k o 'rib
chiqaylik.
t o 'z g a ru v c h in in g qiym atini
/ = /. = / '- r ( r - vaqt b o 'y ic h a
integrallash
qadam i) d eb olib,
y ( t . ) = y i, у ( t , ) = y, , у ( l , ) = y , ,
A ( t J = A., B (t.J = Bi,
F (ti ) = F[ b elgilashlarni kiritam iz.
F unksiya h o silasin i bir necha usul yordam ida taq rib iy chekli ayirm alarga
alm ashtirish m um kin. Shulardan biri m arkaziy chekli ay irm alar usulidir.
Bu usulga
asosan
y ( t + x ) ni r n in g darajalari b o 'y ich a T eylor qato rig a yoyilm asi
Ум = У , + 9> + y J ' , +•■•
(6.19)
dan foydalanam iz. (6 .1 9 ) ni г
1 aniqlikda