can I apply a for loop inside the function so that I can make my program short?

ti = 0;
tf = 10E-6;
tspan = [ti tf];
a = 0.6;
n = 0.05;
tc = 10E-9;
r = 1.5;
F = 10;
 
f = @(t,y) [  
                  (-1/(2*tc)).*(1 - r/(1+ (y(1)^2)./F)).*y(1) + (n/(2*tc)).*((cos(y(6))).*y(2)) ;
                  (-1/(2*tc)).*(1 - r/(1+ (y(2)^2)./F)).*y(2) + (n/(2*tc)).*((cos(y(7))).*y(3) + (cos(y(6))).*y(1));
                  (-1/(2*tc)).*(1 - r/(1+ (y(3)^2)./F)).*y(3) + (n/(2*tc)).*((cos(y(8))).*y(4) + (cos(y(7))).*y(2));
                  (-1/(2*tc)).*(1 - r/(1+ (y(4)^2)./F)).*y(4) + (n/(2*tc)).*((cos(y(10))).*y(5) + (cos(y(8))).*y(8));
                  (-1/(2*tc)).*(1 - r/(1+ (y(5)^2)./F)).*y(5) + (n/(2*tc)).*((cos(y(9))).*y(4));

               
                
                  (a./(2*tc)).*(  r/(1 + (y(2)^2)./F) - r/(1 + (y(1)^2)./F) ) + (n/(2*tc)).*(((y(3)./y(2)).*sin(y(7))) - (y(2)./y(1) + y(1)./y(2) ).*sin(y(6)) );
                  (a./(2*tc)).*(  r/(1 + (y(3)^2)./F) - r/(1 + (y(2)^2)./F) ) + (n/(2*tc)).*(((y(4)./y(3)).*sin(y(8))) - (y(3)./y(2) + y(2)./y(3) ).*sin(y(7)) + (y(1)./y(2)).*sin(y(6)));
                   (a./(2*tc)).*(  r/(1 + (y(4)^2)./F) - r/(1 + (y(3)^2)./F) ) + (n/(2*tc)).*(((y(5)./y(4)).*sin(y(8))) - (y(4)./y(3) + y(3)./y(4) ).*sin(y(8)) + (y(2)./y(3)).*sin(y(6)));
                   (a./(2*tc)).*(  r/(1 + (y(5)^2)./F) - r/(1 + (y(4)^2)./F) ) + (n/(2*tc)).*(((y(3)./y(4)).*sin(y(8))) - (y(5)./y(4) + y(4)./y(5) ).*sin(y(9)));
                      (a./(2*tc)).*(  - r/(1 + (y(5)^2)./F) ) + (n/(2*tc)).*((y(4)./y(5)).*sin(y(9)));


               ];   

can I apply here the "for loop" inside where the function define. so the program will get short.

I wrote 10 equation in this, what if I want 20 equation ? can I apply for loop in this or any method.

    [time,Y] = ode45(f,tspan,[1;1;1;1;1;1;1;1;1;1].*10E-6);
plot(time,Y(:,6))
hold on
plot(time,Y(:,7))
plot(time,Y(:,8))
plot(time,Y(:,9))
hold off

[per isakson]

Moved. Posted as an answer by mistake

"what if I want 20 equation" How do these twenty equations differ?

[per isakson]

Moved

if i =20 the A0 = 0 and A21 =0 and O0 = 0 and O21 = 0 these are the condition, how can I make this short ?

[per isakson]

Now I think I understand your question.

Are there typos in your anonymous function? This looks suspect. e.g. "y(8)" in three rows.

Does your anonymous function agree with the equations in your comment?

[Torsten]

For more details (especially how A_0, phi_0, A_N+1 and phi_N+1 are defined), see

https://de.mathworks.com/matlabcentral/answers/1771405-there-are-two-coupled-differential-equation-i-try-to-solve-that-differential-for-the-i-1-to-5-b?s_tid=prof_contriblnk

Answer 1

[Torsten]

N = 5;
ti = 0;
tf = 10E-6;
tspan = [ti tf];
[time,Y] = ode45(@(t,y)f(t,y,N),tspan,[1;1;1;1;1;1;1;1;1;1].*10E-6);

function dy = f(t,y,N)
  a = 0.6;
  n = 0.05;
  tc = 10E-9;
  r = 1.5;
  F = 10;
  A = y(1:N);
  phi = y(N+1:2*N);

  dA = zeros(N,1);
  dphi = zeros(N,1);

  dA(1) = ...;
  dphi(1) = ...;
  for i = 2:N-1
    dA(i) = ...;
    dphi(i) = ...;
  end
  dA(N) = ...;
  dphi(N) = ...;

  dy = [dA;dphi];
end