clear all;
clc;

lambda = 1;
k_max =15;

a = 0;
b = 5;
n = 500;
step = (b-a)/n;



for i=1 :n+1
    x(i) = a + (i-1) * step;
    y=zeros(1,i);
    real(i)=(5/3)*e^(-x(i))-(2/3)*cos(sqrt(2)*x(i))+((2*sqrt(2))/6)*(sin(sqrt(2)*x(i)));
endfor


for k = 2 : k_max

    for i = 1 : size(x, 2)
         temp = 0;
         for j = 1 : i
              temp = temp + K(x(i)-x(j))*y(k-1,j)*step;
         end
       temp = temp + f(x(i));
       temp = temp * lambda;

        y(k,i) = temp;
    end

end
plot(x,y(k_max,:),x,real);