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why do I get -Inf

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work wolf
work wolf on 17 Jun 2022
Commented: work wolf on 18 Jun 2022
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
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Note: That is code for formula

Accepted Answer

Jan
Jan on 17 Jun 2022
Edited: Jan on 17 Jun 2022
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?
  3 Comments
Torsten
Torsten on 18 Jun 2022
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
work wolf on 18 Jun 2022
@Torsten thank you

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