how can I use summation and index for the series

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work wolf
work wolf 2022-5-24
评论： Torsten 2022-5-25
how can I use summation and index for the following series by using matlab
Edit:
the pervious Equation solution for
My trying to write the following code, but i don't know if it is right ot no
u0=0;
alpha=0.5;%[0.1 0.3 0.5 0.6 0.66 0.9 1]; matrix
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);
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;
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Torsten
Torsten 2022-5-25
A link where the solution scheme for your equation is derived and explained.

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