%Isl f=@(x) (sqrt(1+x.^2))./(1+cos(x)), a=0, b=1, n=4 ch=0, h=(b-a)/n, vx=a:h:b, Isl=h/2*(f(vx(1))+2*sum(f(vx(2:1:n)))+f(vx(n+1))), tab=[n Isl ch] Is=Isl, n=n*2, h=(b-a)/n, vx=a:h:b, Isl=h/2*(f(vx(1))+2*sum(f(vx(2:1:n)))+f(vx(n+1))), ch=abs(Is-Isl), tab=[tab; n Isl ch] %Iss a=1, b=exp(1), n=4, h=(b-a)/n, x=a:h:b Inovy = h/3*(f(x(1))+4*sum(f(x(2:2:n)))+2*sum(f(x(3:2:n)))+f(x(n+1))) I = Inovy, n = 2*n, h = (b-a)/n, x = a:h:b, Inovy = h/3*(f(x(1))+4*sum(f(x(2:2:n)))+2*sum(f(x(3:2:n)))+f(x(n+1))) Chyba = abs(Inovy-I) In=Iss, n=n*2, h=(b-a)/n, vx=a:h:b, Iss=(h/3)*(f(vx(1))+4*sum(f(vx(2:2:n)))+2*sum(f(vx(3:2:n)))+f(vx(n+1))), ch=In-Iss, tab=[tab; n Iss ch] %Runge a=1, b=5, h=0.5, f=@(x,y) (cos(x))./((y.^2)+3), vy(1)=-1 vx=a:h:b, n=(b-a)/h for i=1:n k1=h*f(vx(i),vy(i)) k2=h*f(vx(i)+h/2, vy(i)+k1/2) k3=h*f(vx(i)+h/2, vy(i)+k2/2) k4=h*f(vx(i+1), vy(i)+k3) vy(i+1)=vy(i)+1/6*(k1+2*k2+2*k3+k4) end [vx; vy] plot(vx, vy, '-') %Heune a=1, b=5, h=0.5, f=@(x,y) (cos(x))./((y.^2)+3), vy(1)=-1 vx=a:h:b, n=(b-a)/h for i=1:n k1=h*f(vx(i),vy(i)) k2=h*f(vx(i)+h,vy(i)+k1) vy(i+1)=y(i)+(1/2)*(k1+k2) end [vx; vy] plot(vx, vy, '-')