Differensial tenglamalarni taqribiy yechimlarini aniqlash. Runge –kutta va adams usullari

9.4- Paskal tili dasturi
{Birinchi tartibli differentsial tenglama }
{Y^'=F(X,Y) uchun}
{Koshi masalasini Runge-Kutta usulida taqribiy yechimini topish}


uses crt;
function f(x,y:real):real;
begin
f:=x+y
end;
var
x,y,q1,q2,q3,q4,b,h:real;
i,n:integer;
begin
clrscr;
writeln(' Koshi masalasini Runge-Kutta usulida hisoblash');
x:=0;y:=1;n:=10;b:=2;
h:=(b-x)/n;
for i:=1 to n do
BEGIN
q1:=h*f(x,y);
q2:=h*f(x+h/2,y+q1/2);
q3:=h*f(x+h/2,y+q2/2);
q4:=h*f(x+h,y+q3);
y:=y+(q1+2*q2+2*q3+q4)/6;
x:=x+h;
writeln;
write(' x(',i,')=',x:8:4);
WRITE(' y(',i,')=',Y:8:4);
end;
writeln;
writeln(' ENTER tugmasini bosing');
readln;
end.
O‘z-o‘zini tekshirishuchun savollar:

1. 
   Birinchi tartibli differentsial tenglama taqribiy uchimi Runge-Kutta usuli yordamida qanday topiladi?
   
2. 
   Taqribiy uchim hato;igini baholashni tushintirib bering?
   
3. 
   Birinchi tartibli differentsial tenglama taqribiy uchimini topishda Eyler va Runge-Kutta usulidagi yechim aniqniqlashdagi baholashni tushintirib bering?
   
4. 
   Echim aniqligini baholashni aniqlovchi shartni yozing.