Toshkent axborot texnologiyalari universiteti huzuridagi dasturiy mahsulotlar va apparat dasturiy majmualar yaratish

Trapetsiya usuli

program trapesiya;

var n,i,k:integer; a,b,h,s:real;
function f(x:real):real; begin f:=x*x end; procedure trap(a,b:real;n:integer; var s:real); var i:integer; h:real;
begin h:=(b-a)/n; s:=(f(a)+f(b))/2;
for i:=1 to n-1 do s:=s+f(a+i*h); s:=s*h; end; begin
write('a,b,n=');readln(a,b,n); trap(a,b,n,s);

writeln('S=',s); end.

Programma asosida eksperimentlar o’tkazamiz. a,b,n=0 1 10 S=0.335
a,b,n=0 1 20 S=0.33375
a,b,n=0 1 100 S=0.33335
a,b,n=0 1 1000 S=0.3333335
Natija to’g’riligi ko’rinib turibdi.

1. Simpson formulasining dasturi Simpson usuli

program Simpson_simpl;

var n,i,k,m:integer; a,b,h,s,s1,s2:real; //n=2m

function f(x:real):real;

begin f:=x*x end;

procedure Simp(a,b:real;n:integer; var s:real); var i:integer; h:real;

begin s:=f(a)+f(b); s1:=0;s2:=0; h:=(b-a)/n; m:=n div 2;
for i:=1 to m-1 do
begin s1:=s1+f(a+(2*i-1)*h); s2:=s2+f(a+(2*i)*h) end; s:=s+4*s1+2*s2;s:=s*h/3; end;
begin

write('a,b,n=?'); readln(a,b,n); h:=(b-a)/n; Simp(a,b,n,s); writeln('S=',s);

end.

Programma asosida eksperimentlar o’tkazamiz.

a,b,n=?0	1	10	S=0.225333333333333
a,b,n=?0	1	20	S=0.273166666666667
a,b,n=?0	1	40	S=0.301645833333333
a,b,n=?0	1	80	S=0.317080729166667
a,b,n=?0	1	100	S=0.320265333333333
a,b,n=?0	1	200	S=0.326733166666667
a,b,n=?0	1	500	S=0.330677322666667

Natija to’g’riligi ko’rinib turibdi.

Nazariy savollar va topshiriqlar

1. Nyuton-Kotes kvadratura formulasini yozing.

   
   

2. Chap va ung to’g’ri to’rtburchaklar formulasini yozing.

   
   

3. Markaziy to’g’ri turtburchaklar formulasini yozing.

   
   

4. Trapetsiya formulasini yozing.

   
   

5. Simpson formulasini yozing.

   
   

1. ma’ruza. Oddiy differensial tenglamalarni taqriban yechish. Funksiya hosilasiga ko‘ra yechilgan birinchi tartibli oddiy differensial tenglamalar uchun Koshi masalasini taqriban yechish. Eyler va Runge-Kutta usullari. Ularning algoritmi va dasturlari. Taqribiy yechimning geometrik ifodasi

REJA:

1.