Maruza mashg’ulotlari

algoritm asosida paskal dasturlah tilidagi dasturi

Program Eyler;

var a,b,x0,y0,x,y,h:real;

Function f(x,y:real):real;

Begin

f:=<функция куриниши>;

end;

Begin

Write(‘a,b=’); readln(a,b);

Write(‘y0=’); readln(y0);

x0:=a;

Write(‘h=’);readln(h);

writeln(‘x0=’,x0,’ y0=’, y0 );

x:=x0;y:=y0;

while x< b do

begin

y:=y+h*f(x,y);

Writeln(‘x=’,x; ‘ y=’,y);

x:=x+h;

end;

Readln;

end.

Runge-Kutta usuliga mos blok-sxema.

algoritm asosida paskal dasturlah tilidagi dasturi:

Program R__kutta;

var a,b,x0,y0,h,x,y,k0,k1,k2,k3:real;

function f(x,y:real):real;

begin

f:=. . .;

end;

Begin

Write(‘a,b=’);readln(a,b);

Write(‘y0,h=’);readln(y0,h);

x:=a;y:=y0;

while x

begin

k0:=f(x,y);

k1:=f(x+h/2,y+h*k0/2);

k2:=f(x+h/2,y+h*k1/2);

k3:=f(x+h,y+h*k2);

y:=y+(k0+2*k1+2*k2+k3)*(h/6);

x:=x+h;

Writeln(‘x=’,x,’ y=’,y );

end;

readln;

end.
To’rtinchi bob bo`yicha savol va topshiriqlar

1. 
   Aniq integralning geometrik ma’nosi qanday?
   
2. 
   Aniq integralni nima uchun taqribiy hisoblanadi?
   
3. 
   Aniq integralni taqribiy hisoblash usullari qaysilar?
   
4. 
   To‘gri to‘rtburchaklar usuliga mos ishchi formulalarni qanday hosil qilinadi ?
   
5. 
   Qanday tenglamalarni differensial tenglamalar deb ataymiz?
   
6. 
   Oddiy differensial tenglamalarga ta’rif bering?
   
7. 
   Umumiy echim nima?
   
8. 
   Xususiy echim nima?
   
9. 
   Differensial tenglamalarni taqribiy echish zaruriyati qaerdan kelib chiqadi?
   
10. 
    Differensial tenglamalar ni taqribiy echishning qanday usullarini bilasiz?
    
11. 
    Eyler usulining ishchi algoritmi?
    
12. 
    Runge-Kutta usulining ishchi algoritmi?
    
13. 
    Runge-Kutta usulining qanday kamchiligi va afzalligi bor?
    
14. 
    Amaliy topshiriqlar
    

Eyler va Runge-Kutta usullari yordamida berilgan differensial tenglama uchun Koshi masalasini h0.1 =adam bilan [0;1] orali=da yechimini topish algoritmi va dasturini tuzing.

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