why do I get -Inf

why I got -INF by the following code

clear all
clc
u0=0;
alpha=0.5;%[0.1 0.3 0.5 0.6 0.66 0.9 1];
a=0; b=1;n=100; 
h=(b-a)/n;
t=a:h:b;
f=@(t,u) (-u.^4) +  ( gamma(2*alpha+1)./gamma(alpha+1) ).*(t.^alpha) - ...
         ( 2./gamma(3-alpha) ).*(t.^(2-alpha)) + (t.^(2*alpha)-t.^2).^4;
exact=@(t) t.^(2*alpha)-t.^2;
%-----a'ks---------------------------------------
a_kth=@(k) (k+1).^(1-alpha)-(k).^(1-alpha);
u_p=zeros(1,n); z_p=zeros(1,n); u=zeros(1,n);
s=0;
for i=1
    u_p(i)=a_kth(i-1)*u0;    %s=s+q^keval(subs(fun,xq^k));
    z_p(i)=gamma(2-alpha)*( h.^alpha ) * f(t(i),u_p(i));
    u(i)=u_p(i)+gamma(2-alpha)*( h.^alpha ) * f(t(i),u_p(i)+z_p(i));
end
%--------------------------------------
for i=2:n
for k=1:i-1
    s=s+(a_kth(i-1-k)-a_kth(i-k))*u(k);
    WW(i,k)=s;
    u_p(i)=a_kth(i-1)*u0+s;    %s=s+q^keval(subs(fun,xq^k));
    z_p(i)=gamma(2-alpha)*( h.^alpha ) * f(t(i),u_p(i));
    u(i)=u_p(i)+gamma(2-alpha)*( h.^alpha ) * f(t(i),u_p(i)+z_p(i));
end
end
u1=[ u0 u];
%plot(t,u1)
exact1=exact(t);
error=exact1-u1;
WW

Result:

0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0	0.00577975952460106	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0.00577975952460106	0.00673067252184994	0.0181797346976039	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0.0181797346976039	0.0186719634854510	0.0205556165998920	0.0409452936234420	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0.0409452936234420	0.0412598549444615	0.0422349055452296	0.0455895103188147	0.0806650433967495	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0.0806650433967495	0.0808884860242097	0.0815115970908744	0.0832480682992657	0.0890188586145502	0.148491438540129	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0.148491438540129	0.148660752484077	0.149103367531229	0.150213068326286	0.153200249204064	0.162984955469167	0.263126255687181	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0.263126255687181	0.263260301799387	0.263595693931748	0.264383948700448	0.266292921897948	0.271357858562234	0.287833572393128	0.455671522228742	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0.455671522228742	0.455781071221356	0.456046601693089	0.456643902777675	0.457999905434385	0.461236679079759	0.469765136121947	0.497378618525665	0.776417293874955	0	0	0	0	0	0	0	0	0	0	0	0	0
0.776417293874955	0.776509006663904	0.776726011060435	0.777198895256139	0.778226408047328	0.780525588396241	0.785975742429658	0.800269532725029	0.846178277197070	1.29815227837924	0	0	0	0	0	0	0	0	0	0	0	0
1.29815227837924	1.29823052627514	1.29841219913169	1.29879866306123	1.29961214653275	1.30135435345696	1.30522576629736	1.31436028599369	1.33812440080591	1.41248527175795	2.11994060975294	0	0	0	0	0	0	0	0	0	0	0
2.11994060975294	2.12000839676635	2.12016339716412	2.12048693902389	2.12115175722225	2.12253106514812	2.12546463330435	2.13195316493602	2.14713974388620	2.18563176311180	2.30202561531432	3.55958603674999	0	0	0	0	0	0	0	0	0	0
3.55958603674999	3.55964550477269	3.55977978332318	3.56005582410283	3.56061240002069	3.56173963744143	3.56406214790374	3.56897884125577	3.57976633760707	3.60436485909801	3.66461475046373	3.87151445701363	-659.195564987181	0	0	0	0	0	0	0	0	0
-659.195564987181	-659.195512264164	-659.195394464610	-659.195155327445	-659.194680465706	-659.193736759285	-659.191838690947	-659.187946137189	-659.179771897684	-659.162298807681	-659.123795806867	-659.016696637904	-768.107585490216	-4.07091948703171e+39	0	0	0	0	0	0	0	0
-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.07091948703171e+39	-4.74068615024585e+39	-Inf	0	0	0	0	0	0	0
-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	0	0	0	0	0	0
-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	0	0	0	0	0
-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	0	0	0	0
-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	0	0	0
-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	0	0
-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	-Inf	0
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Note: That is code for formula

Answer 1

[Jan]

alpha = 0.5;
u0    = 0;
a_k   = @(k) (k + 1)^(1 - alpha) - (k)^(1 - alpha);
n     = 100;
a     = 0;
b     = 1; 
h     = (b - a) / n;
t     = a:h:b;

f = @(t,u) (-u.^4) + (gamma(2*alpha+1) ./ gamma(alpha+1) ) .* (t.^alpha) - ...
         (2./gamma(3 - alpha) ) .* (t.^(2 - alpha)) + (t.^(2*alpha) - t.^2).^4;

up = zeros(1, n);
uc = zeros(1, n);
zp = zeros(1, n);
uc = zeros(1, n);  % ??? is this your "u"?

C = gamma(2 - alpha) * h ^ alpha;
for ni = 1:n
   up(ni) = a_k(ni - 1) * u0;
   for k = 1:ni - 1
       up(ni) = up(ni) + (a_k(ni - 1 - k) - a_k(n - k)) * uc(k);
   end

   zp(ni) = C * f(t(ni), up(ni));
   uc(ni) = up(ni) + C * f(t(ni), up(ni) + zp(ni));
end
fprintf('%g\n', up(1:20))

0
0
0.00936959
0.025553
0.0510836
0.0900857
0.148774
0.236353
0.366246
0.557332
0.833188
1.21388
1.71671
2.49653
3.66575
-1917.46
-1.72608e+47
-Inf
-Inf
-Inf

I've implemented the formula from the image again and get the same behavior for up. This means, that your output is mostlikely mathematically correct. What you you expect instead?

[work wolf]

@Jan thank you so much, your answer correct with replace

n

by

ni

as follows, replace

up(ni) = up(ni) + (a_k(ni - 1 - k) - a_k(n - k)) * uc(k);

by

up(ni) = up(ni) + (a_k(ni - 1 - k) - a_k(ni - k)) * uc(k);

gives without -Inf,

0
0
0.00577976
0.0124
0.0193799
0.0265306
0.0337538
0.0409904
0.0482015
0.0553596
0.0624445
0.0694409
0.0763364
0.0831215
0.089788
0.0963293
0.10274
0.109015
0.11515
0.121141

My Question: why I got -INF by the my code.

Please, how can i use alpha as matrix with your answer as,

alpha = [0.1 0.3 0.5 0.6 0.66 0.9 1];

[Torsten]

Step through your code and output the values of the variables involved in the calculation of "up".

That's called "debugging" and we also had to do this tedious job in order to answer your question.

[work wolf]

@Torsten thank you