least square approcah for method of moments fourth order non linear differential equations

hi

plz help

How can we apply least square approach for the convergence of solution for this given code.

%%MoM Solution

syms f(x)

%MoM Solution

syms k(x)

k = 1*x^2+1*x+1.05;

%L=diff(y,x,2)

%weight n is chosen to satisfy the boundary conditions stated above

N = 1;

for n = 1:N

t(n) = x - x^(n+1);

end

%For Galerkin's Mom the weighting functions are the same as the basis

%functions

M = N; %M=N

%for j=1:N

% weight(j)=basis(j);

for m = 1:M

w(m) = x - x^(m+1);

end

%Create Matrix Z

for i = 1:M

for j = 1:N

%-((9*(x.^2)+6)*f(4))-(((8*x)+3)*f(3))-(f(1)*f(2))-f(1)+(20*(x^2))+(13*x)+36];

temp = w(i).*(-(9*(x.^2)+6)*(diff(t(j),x,4))-((8*x+3)*(diff(t(j),x,3))- t(j)*diff(t(j),x,2) -1*(diff(t(j),x,1))));

% + w(i-1).*((a*x+b)*(diff(t(j),x,1)))+w(i-2).*(diff(t(j),x,0) +(a*x+b)*(diff(t(j),x,1))+(diff(t(j),x,0)))];

Z(i,j) = int(temp, 0, 1);

end

end

%Create' Vector V

for i = 1:N

temp = k*w(i);

V(i) = int(temp, 0, 1);

end

I = inv(Z)*V';

f(x) = 0;

for n = 1:N

f(x) = f(x) + I(n) * t(n);

end

ezplot(f(x), [0 10])

axis([0 10 0 140]);

title('MOM for N=1')

%legend('N=3')