paragraph3task5

//main
format long;
a=0; b=10; n=201;
x=linspace(a,b,n);
f=@(x) 0;
K=@(x,s,y) (1+y^2)/(1+s^2);
tol=1e-07;
u=@(x) x;
[y,x,iter]=Nonlin_VoltII_SimpleIter_Simpson(a,b,n,K,f,tol);
er=norm(u(x)-y,inf)/norm(u(x),inf)
plot(x,y,'o',x,u(x),'r');
xlabel('x');
ylabel('y');

//function
function [y,x,iter]=Nonlin_VoltII_SimpleIter_Simpson(a,b,n,K,f,tol,y0)
x=linspace(a,b,n);
h=x(2)-x(1);
F=f(x);
if(nargin<=6) y0=F;
end
if(nargin<=5) tol=1e-10;
end
y=ones(1,n)*inf;
yk=y0;
iter=0;
yk(1)=F(1);
y(1)=F(1);
while(norm(yk-y,inf)/norm(yk,inf)>tol)
    y=yk;
    iter=iter+1;
    for i=2:n
        s=f(x(i));
        for j=1:(i-1)
            s=s+h*K(x(i),x(j),yk(j));
        end
        fun = @(y_i) (y_i-(h/2)*K(x(i),x(i),y_i)-s);
        yk(i)=fsolve(fun,yk(i-1));
    end
end