clear
valg=5;  %1=euler ekspl  2=euler impl  3=trapes  4=heun  5=RK4
plotte=0;  %plotte=1  ikke plotte=0

n=4;
h=1/n;
x=linspace(0,1,n+1);
y=zeros(1,n+1);
y(1)=1;

if valg==1    
    figure;hold on
    for i = 1:n        
        y(i+1)=(1-h)*y(i);
        plot(x(1:i),y(1:i),'d');
        axis([0 1 0 1])
        pause
    end
    plot(x,y,'d');
    plot(x,exp(-x))
    axis([0 1 0 1])
    pause
    
end

if valg==2    
    for i = 1:n
        y(i+1)=y(i)/(1+h);
    end    
end


if valg==3    
    for i = 1:n
        y(i+1)=(2-h)*y(i)/(2+h);
    end    
end

if valg==4    
    for i = 1:n
        y_star=(1-h)*y(i);
        y(i+1)=y(i)-h*(y(i)+y_star)/2;
    end    
end

if valg==5    
    for i = 1:n
        k_1=-h*y(i);
        k_2=-h*(y(i)+k_1/2);
        k_3=-h*(y(i)+k_2/2);
        k_4=-h*(y(i)+k_3);
        y(i+1)=y(i)+(k_1+2*k_2+2*k_3+k_4)/6;
    end    
end


if plotte==1
    figure
    plot(x,y); hold on
    plot(x,exp(-x))
end
disp(y(end)-exp(-1))