clear all;
h=0.01;
x=(0:h:2);
y=zeros(1,length(x));
y(1)=1;
y2=y;
blad(1)=0;
e=exp(x.*x);
for i=(1:length(x)-1);
    %y2(i+1)=y2(i)+h*f(x(i),y2(i));
    y2(i+1)=y2(i)+h/2*(f(x(i),y2(i))+f(x(i)+h,y2(i)+h*f(x(i),y2(i))));
    blad(i+1)=abs(y2(i+1)-e(i+1));
  %  y3(i+1)=y3(i)+h*f(x(i)+h/2,y3(i)+h/2*f(x(i),y3(i)));

end


h=0.05;
x1=(0:h:2);
y=zeros(1,length(x1));
y(1)=1;
y3=y;
e1=exp(x1.*x1);
blad1(1)=0;
for i=(1:length(x1)-1);
    %y3(i+1)=y3(i)+h*f(x1(i),y3(i));
    y3(i+1)=y3(i)+h/2*(f(x1(i),y3(i))+f(x1(i)+h,y3(i)+h*f(x1(i),y3(i))));
    blad1(i+1)=abs(y3(i+1)-e1(i+1));

    %
    %y3(i+1)=y3(i)+h*f(x(i)+h/2,y3(i)+h/2*f(x(i),y3(i)));

end


h=0.1;
x2=(0:h:2);
y=zeros(1,length(x2));
y(1)=1;
y4=y;
e2=exp(x2.*x2);
blad2(1)=0;
for i=(1:length(x2)-1);
     y4(i+1)=y4(i)+h/2*(f(x2(i),y4(i))+f(x2(i)+h,y4(i)+h*f(x2(i),y4(i))));
     blad2(i+1)=abs(y4(i+1)-e2(i+1));

     %
     %y3(i+1)=y3(i)+h*f(x(i)+h/2,y3(i)+h/2*f(x(i),y3(i)));

end


h=0.5;
x3=(0:h:2);
y=zeros(1,length(x3));
y(1)=1;
blad3(1)=0;
e3=exp(x3.*x3);
for i=(1:length(x3)-1);
   y(i+1)=y(i)+h/2*(f(x3(i),y(i))+f(x3(i)+h,y(i)+h*f(x3(i),y(i))));
   blad3(i+1)=abs(y(i+1)-e3(i+1));
   %

end


plot(x,blad,'r',x1,blad1,'b',x2,blad2,'c',x3,blad3,'m');
hold on;
legend('h=0.01','h=0.05','h=0.1','h=0.5','Funkcja e^x^2')
%plot(x,y,'b',x,y2,'r',x,y3,'g',x,y4,'black');
%legend('Metoda Eulera','Udoskonalona metoda Eulera','Zmodyfikowana metoda Eulera','Funkcja e^x^2')

grid on;