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.

program chekli ayirma:
const nt= 21; d t = l ; C 0 = -I; D 0= 3.0;
type m a s = a r r a y [l..n t] o f real;
v a ry ,t:m a s ; i:integer;
fu n ction a(x: real) .real;
begin
a: = x + l ;
{A(t) -fu n k s iy a ко 'rinishi}
end;
fu n ction b (x:real).real;
begin
b:= x -2 ;
{B(t) -f u n k s iy a к о 'rinishi}
end;
fu n ction f(x : real): real;
begin
f:= x * x * x + 3 * x * x -2 * x + 7 ;
{ F(i) - fu n ksiya ko'rinishi}
end;
begin
f o r i: = I to nt d o t[ i] ; = ( i- l) * d t;
У Щ .-C O ;
у [ 2 ] : = 1/4 *((4-2 *b(0) *sqr(dt)) *C0-2 *dt *(a(0) *dt-2) *D 0+ 2 *sqr(dt) *f(0));
f o r i: = 2 to nt-1 d o
y [ i + 1 ]: = L '(2 + a (t[i])* d t) *((4-2*b(t[i]) *sqr(dt)) * y [i]+
(a (t[ij) *dt-2) *y[i- 1J+2 *sqr(dt) *f(t[ij));
f o r i: = l to nt d o w rite ln ('t= ',t[i]:4 :2 ,' y = ',y [ij:8 :7 );
end.
S a v o lla r
1. D ifferensial ten g lam ag a t a ’r if bering.
2. D ifferensial ten g lam an in g tartibi qanday aniqlanadi?
3. D ifferensial tenglam a uchun b o sh lan g 'ich shartlar qanday beriladi?
4. D ifferensial ten g lam a uchun chegaraviy shartlar qanday b eriladi?
5. K oshi m asalasi qanday m asala?
6
. B o sh la n g 'ic h shartli chegaraviy m asalalar qanday b o 'la d i?
7. D ifferen sial ten g lam an i y ech ish d a o peratsion hisob usuli?
8
. T a sv ir fu n k siy a nim a?
9. Q anday fu n k siy alar original fun k siy alar deb ataladi?

10. T a sv ir fu n k siy a uchun chiziqlilik xossasi.
11. T a sv ir fu n k siy a uchun siljish xossasi.
12. T a sv ir funksiyani differensiallash.
13. S onli differen siallash nim a?
14. S onli differensiallashda xatolik qanday aniqlanadi?
15. D ifferensial tenglam alarni yech ish d a E yler usuli va uning algoritm i?
16. D ifferensial tenglam alarni y ech ish d a R unge-K utta usuli va uning algoritm i?
17. C h ek li ay irm alar usuli va uning algoritm i.
M iso l v a m a s a la la r
1.
B erilg an differensial tenglam alarni berilgan shartlarni q anoatlantiruvchi
y ech im in i operatsion hisob usuli y o rd am id a aniqlang:

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