O ’z b e k ist o n r e sp u b L ik a si o L iy va o ’r t a m a X su s t a ’lim V a z ir L ig I o ’zbek jsto n r e sp u b L ik a si

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Bog'liq
boshqarish tizimlarini kompyuterli
Elektr mash. fan.

\a ,b \
= a - ^ f ( a )

pro gram oraliq2; u ses c r t;
var a,b,eps,x,fa,fc,c:real;
function f(x :re a l):re a l;
begin
f: =x*x-sin(x)-0.5
{ f(x ) fun ksiyan in g ко 'rinishi}
end;
begin clrscr;
w r ite ( 'a - ) ; read(a); { a ning qiym atin i kiritish}
writef'b '); read(b); { b ning qiym atin i kiritish}
w rite ('e p s= ); rea d (ep s); { e n ing qiym atini kiritish}
fa := f(a );
while a b s(b -a )> e p s do
begin
c:= (a + b )/2 ; fc := f(c );
i f fa * fc < = 0 then b :~ c else begin a : = c ; fa := f c end;
end;
writeln('x \c :l();4 ); { tenglam aning ta q rib iy ildizini chop qilish}
end.
M isol: Y uqorida keltirilgan dasturdan foydalanib
x~ - sin x - 0,5 = 0
tenglam aning [
0
;
2
] oraliqdagi y echim ini
0 , 0 0 1
aniqlikda hisoblang.
J a v o b : x = 1,1963.
65

4.6. Transsendent tenglamalarni yechishda vatarlar usuli
(4.8)
te n g la m a n in g \a ,b \ oraliqdagi e an iq lik d ag i taq rib iy yechim ini topish
talab etilsin. A n iq lik uchun f ( a ) > 0 ( f ( a ) < O) b o ‘lsin. A = A ( a ; f ( a ) ) ,
В = B (b ; f ( b ) ) nuq talard an to ‘g ‘ri chiziq o ‘tk a z a m iz (4.2-rasm ) v a b u to ‘g ‘ri
chiziqni O x o ‘ qi b ilan kesishish nuqtasini x, = a -
^
~ f ( a ) deb belgi-
laym iz.
A g ar \ a - x \ < £ b o 'ls a , x = x, (4.8) te n g la m a n in g s aniqlikdagi taqribiy
yechim i d eb q ab u l qilinadi. B u shart b ajarilm asa, b = x t (a = x ,) deb olam iz v a

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