How to vectorized the following for loop code?

for n=1:nt-1
    sum1=0;
    for jj=1:m-1
        sum1=sum1+(t(n+1)).^jj.*u(1).^jj/factorial(jj);
    end
    sum2=0;
    for ii=1:n
        sum2=sum2+(h.^alpha).*(1/gamma(alpha+1)).*((n-ii+1).^alpha-(n-ii).^alpha).*(f(t(ii),u(ii)));

    end
    u(n+1)=sum1+sum2;
end

Answer 1

[Jan]

As in your other threads: Start with cleaning the loop. You should try to do this by your own.

u1c = u(1);
c1  = (h .^ alpha) .* (1 / gamma(alpha+1));
for n = 1:nt-1
  tn1c = t(n + 1);
  tn1  = 1;
  u1   = 1;
  fact = 1;
  sum1 = 0;
  for jj = 1:m-1
    fact = fact * jj;   % A faster factorial(jj)
    tn1  = tn1 * tn1c;  % A faster t(n+1)^jj
    u1   = u1 * u1c;    % A faster u(1) ^jj
    sum1 = sum1 + tn1 .* u1 / fact;
  end

    sum2 = 0;
    v    = -diff((n:-1:0) .^ alpha);
    for ii=1:n
        sum2 = sum2 + c1 .* v(ii) .* f(t(ii), u(ii));
    end
    u(n+1) = sum1 + sum2;
  end

Is f a function or a matrix?

[Pooja Patil]

f is a function.for example:

f=@(t,u)(t.^(4-0.1))/(gamma(5-0.1))-u;

[Jan]

@Pooja: Please note that the gamma function is very expensive. Do not use it to calculate constants repeatedly.