why do I get -Inf

7 次查看（过去 30 天）
work wolf
work wolf 2022-6-17
评论： work wolf 2022-6-18
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

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采纳的回答

Jan
Jan 2022-6-17
编辑：Jan 2022-6-17
Ran in:
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 个评论
显示 1更早的评论
Torsten
Torsten 2022-6-18
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.

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