Combining for-loops/while-loops and ODE45

Question

I was wondering if it's possible to combine for-loops/while-loops and ODE45?, please look at the example below:

I have a function (ode) which I want to solve at different ic (initial conditions):

ser = @(x) x.^(-0.3) - x.^(1.8); % the function
tspan = 1:0.02:2; 
x0 = 0.5;
% x0 = 0.8;
% x0 = 1.2; 
% x0 = 1.8;
% x0 = 2; 
% x0 = 2.5; 
[~, x_t] = ode45(@(t,x) ser(x), tspan, x0);
plot(tspan,x_t,'r-') 

And plot the solution curves at the end.

Is there a way to pass the other icwithout doing it manually, like a loop? or any other way to optimize this step? If I could receive some help with this, it will be very appreciated because I have to compute many ODEs (more complex ones) at 15 to 25 different ic.

Thanks in advance!

PS. If the code has to change (e.g. different names for the x0s or solutions x_t) it will be OK!

Answer 1

If you have a predefined no. of ic you can use this for loop:

 for i=1:NoOfic
      test_mat(i,:)=test_ode_45(x(i),tspan);
  end

You should predefine your matrix (test_mat) in a sufficient dimension e.g.

test_mat = zeros(NoOfic, SizeOftspan)

Obviously I have defined the variables NoOficand SizeOftspanto the specific numbers

My whole test-code is:

tspan = 1:0.02:2;
x= [0.4 0.8 1.2 1.5 2.6];
sizeOftspan = size(tspan);
sizeOfFamily= size(x);
test_mat = zeros(sizeOfFamily(2),sizeOftspan(2));

test_tes= test_ode_45(x(1),tspan);
  for i=1:sizeOfFamily(2)
      test_mat(i,:)=test_ode_45(x(i),tspan);
  end
plot(tspan, test_mat)

Where my test_ode_45 function is a simple x*sin(t) function