Mavzu: Birinchi tartibli, oddiy differentsial tenglamalarni yechishning sonli taqribiy usullari uchun dastur ta`minotini yaratish

Eyler usuliga mos algoritm blok-sxemasi.

Algoritmning dastur matni:

Program Eyler;

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

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

Begin

f:=;
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 xbegin
y:=y+h*f(x,y);
Writeln(‘x=’,x; ‘ y=’,y); x:=x+h;
end; Readln;
end.
3. Runge-Kutta usulining ishchi algoritmi va dastur ta`minoti.
Bir qadamli oshkor usullarning boshqa bir necha xillari ham majud bo’lib, ularning ichida amalda eng ko’p ishlatiladigani Runge-Kutta usuli hisoblanadi. Usul shartiga ko’ra har bir yangi x_i1 tugun nuqtadagi y_i1 yechimni topish uchun f(x,y) funktsiyani 4 marta har xil argumentlar uchun hisoblash kerak. Bu jihatdan Runge-Kutta usuli hisoblash uchun nisbatan ko’p vaqt talab qiladi. Lekin Eyler usulidan ko’ra aniqligi yuqori bo’lganligi uchun, undan amalda keng foydalaniladi.

Runge-Kutta usuliga mos blok-sxema.

Algoritmning dastur matni:

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.