how can i convert from one value to multi values

how can i replace value of

alpha = 0.5

by multi values as

alpha =[0.1 0.3 0.5 0.6 0.66 0.9 1]

in the following code:

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(ni - 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))

[Muhammad Usman Saleem]

try to use intp1 functio in matlab

[work wolf]

@Muhammad Usman Saleem thank you

Answer 1

[Image Analyst]

Try this:

% Define all the alphas that we want to use.
allAlpha =[0.1 0.3 0.5 0.6 0.66 0.9 1]
% Iterate the code for each value of alpha.
for kk = 1 : length(allAlpha)
    alpha = allAlpha(kk);
    % Existing code below:
    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(ni - k)) * uc(k);
        end % of k loop
        zp(ni) = C * f(t(ni), up(ni));
        uc(ni) = up(ni) + C * f(t(ni), up(ni) + zp(ni));
    end % of ni loop
    fprintf('%g\n', up(1:20))
end % of kk loop

[work wolf]

@Image Analyst Thank you so much. Please, how can i store every

up at allAlpha(kk) separated,

meaning

output=[ up(1:20)  at (allallAlpha(1))'  up(1:20)  at (allAlpha(2))'   up(1:20)  at (allAlpha(3))'   up(1:20)  at (allAlpha(4))' ...
         up(1:20)  at (allAlpha(5))'     up(1:20)  at (allAlpha(6))'   up(1:20)  at (allAlpha(7))'];

This is useful for comparison between result.

[Image Analyst]

Is that a matrix, row vector, or column vector? I don't understand what you put. Like (allAlpha(5))' is the same as allAlpha(5) since allAlpha(5) is just a scalar and there is no need to transpose it with '.

[work wolf]

@Image Analyst i want result as matrix including every column at evey iteration,meaning up at alpha=0.1 then alpha=0.3 and so on as follows

0                   0                   0                   0                   0                   0                       0
0                   0                   0                   0                   0                   0                       0
0.0497389463654563	0.0213889960049408	0.00577975952460106	0.00286678264632385	0.00185596757939561	0.000217889077015351	0
0.0756032841848556	0.0394787481302252	0.0123999751730029	0.00655408489750118	0.00438988350200604	0.000568453154565168	0
0.0937806925446395	0.0556290379398444	0.0193798935286129	0.0107113922486972	0.00734884592892711	0.00102120965764830	    0
0.107860035746299	0.0704308289266767	0.0265305609236315	0.0151729898408803	0.0106037797699722	0.00155716732200875  	0
0.119276626823768	0.0841960303939159	0.0337537642308159	0.0198414190139364	0.0140747131135280	0.00216271878416734 	0
0.128782977112920	0.0971145894937620	0.0409904050975548	0.0246522821978120	0.0177066747337709	0.00282736971807349 	0
0.136836519308874	0.109313451384330	0.0482014917128138	0.0295597555016475	0.0214592905356894	0.00354264272057228 	0
0.143742977513616	0.120882992733044	0.0553596049729811	0.0345295051483806	0.0253015035929395	0.00430146626493324 	0
0.149720693652571	0.131890546165088	0.0624445380331634	0.0395348080402283	0.0292085925801107	0.00509780051317483 	0
0.154933371449271	0.142388021211973	0.0694408532510186	0.0445542468881334	0.0331603538578347	0.00592639232345276 	0
0.159508321299395	0.152416520942504	0.0763364150931947	0.0495702537425901	0.0371399266969435	0.00678260656294221 	0
0.163547351524805	0.162009299532333	0.0831214599873308	0.0545681439491122	0.0411329985829613	0.00766230529256888 	0
0.167133636814165	0.171193743128752	0.0897879802538048	0.0595354498177205	0.0451272473771931	0.00856175844777340 	0
0.170336250166931	0.179992745424877	0.0963293011057279	0.0644614459321516	0.0491119375908007	0.00947757605512695 	0
0.173213269808024	0.188425691974366	0.102739781309983	0.0693368016829291	0.0530776205939369	0.0104066556516299      0
0.175813980719025	0.196509182520684	0.109014595844465	0.0741533209796437	0.0570159070743530	0.0113461407282561  	0
0.178180480530615	0.204257572561355	0.115149574557707	0.0789037433441743	0.0609192910387687	0.0122933873534719  	0
0.180348881531626	0.211683386918866	0.121141080069081	0.0835815892474123	0.0647810114200892	0.0132459369880677  	0

[Image Analyst]

You can just index the matrices with kk

zp(kk, ni) = C * f(t(ni), up(ni));
uc(kk, ni) = up(ni) + C * f(t(ni), up(ni) + zp(ni));

assuming zp and uc are row vectors in your original code. Using kk as the first argument would load them into the kk'th row of a matrix.

[work wolf]

i did it, but give me all output, zores !!

% Define all the alphas that we want to use.
allAlpha =[0.1 0.3 0.5 0.6 0.66 0.9 1];
% Iterate the code for each value of alpha.
for kk = 1 : length(allAlpha)
    alpha = allAlpha(kk);
    % Existing code below:
    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(kk, n+1);
    uc = zeros(kk, n+1);
    zp = zeros(kk, n+1);
%     uc = zeros(kk, n+1);  % ??? is this your "u"?
    C = gamma(2 - alpha) * h ^ alpha;
    for ni = 1:n+1 %length(t)
%         up(ni) = a_k(ni - 1) * u0;
          up(kk,ni) = a_k(ni - 1) * u0;    %modfied
        for k = 1:ni - 1
%             up(ni) = up(ni) + (a_k(ni - 1 - k) - a_k(ni - k)) * uc(k);  
            up(kk,ni) = up(kk,ni) + (a_k(ni - 1 - k) - a_k(ni - k)) * uc(kk,k);  % modfied
        end % of k loop
%         zp(ni) = C * f(t(ni), up(ni));
%         uc(ni) = up(ni) + C * f(t(ni), up(ni) + zp(ni));
        zp(kk, ni) = C * f(t(ni), up(kk,ni));                   % modfied
        uc(kk, ni) = up(kk,ni) + C * f(t(ni), up(kk,ni) + zp(kk,ni)); % modfied
    end % of ni loop
%     fprintf('%g\n', up(1:20)) 
end % of kk loop
up

gives,

up =

  Columns 1 through 13

     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     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

  Columns 14 through 26

     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     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

  Columns 27 through 39

     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     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

  Columns 40 through 52

     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     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

  Columns 53 through 65

     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     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

  Columns 66 through 78

     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     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

  Columns 79 through 91

     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     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

  Columns 92 through 101

     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     0     0     0     0
     0     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0

[work wolf]

@Image Analyst thank you so much again. it's done with edite

 up = zeros(kk, n+1);
 uc = zeros(kk, n+1);
 zp = zeros(kk, n+1);
 

before loop (for kk = 1 : length(allAlpha) ) and replace kk by length(allAlpha).

Best regards

Answer 2

[Ayush Kumar Jaiswal]

You want to calculate that function at different values of alpha, it can done using

arrayfun (func, arr);

Read the documentation here.

[work wolf]

@Ayush Kumar Jaiswal thank you