MATLAB: Ode 45 in a loop

for looplength 0ode45

I am trying to solve an ode in a loop, trying to get a single vx and tx value as ouput. I wish to use a loop because a parameter is to be changed everytime a new loop starts. I am getting length 0 output after calling the ode45 function. I wish to integrate the ODE over just one time interval that I have specifed (t(i:i+1)) to get a single value ouput in tx and vx Can you explain how to rectify the issue?
t = linspace(1,10);
vf(1) = 30 ; %some random constant value
vfx = vf(1); % needed in the function ode_research_x
x(1) = -3;% starting point for x
for i = 1:length(t)-1
    vfx = vf(1); % this vfx is then used by the ode_research_x function
    [tx,vx] = ode45('ode_research_x', t(i:i+1), vp(1)); % I am not sure but the time step seems like an issue
    x(i+1) =  x(i) + vx.*tx;
    vp(1) = vx;
    vf(1) = 30; % some new constant value calculated in the loop (I've shown a random value)
end
%function to define the ode
function dudt = ode_research_x(vx,vfx)
dudt = 18*mu_f*Cd*Rep*(vx - vfx)/(rho_p*d^2*24); % all the variables except vx and vfx are constant values in the same workspace so I haven't shown their values but they are defined 
end

Best Answer

You have a couple of problems with your code. Your ode_research does not follow the ordinary form (dydy = ode_f(t,y)) that ode45 expects. Then your use of a string for the first argument is a bit arcane. I would expect something like this would be better:
t = linspace(1,10);
vf(1) = 30 ; %some random constant value
vfx = vf(1); % needed in the function ode_research_x
x(1) = -3;% starting point for x
vp = v_initial; % or whatever you have as initial condition
for i = 1:length(t)-1
    vfx = vf(1); % this vfx is then used by the ode_research_x function
    [tx,vx] = ode45(@(t,vx) ode_research_x(t,vx,vfx), t(i:i+1), vp(1)); % I am not sure but the time step seems like an issue
    x(i+1) =  x(i) + vx(end).*tx;
    vp(1) = vx;
    vf(1) = 30; % some new constant value calculated in the loop (I've shown a random value)
end
%function to define the ode
function dudt = ode_research_x(t,vx,vfx)
% Some initialization of the constants, I assume.
dudt = 18*mu_f*Cd*Rep*(vx - vfx)/(rho_p*d^2*24); % all the variables except vx and vfx are constant values in the same workspace so I haven't shown their values but they are defined 
end
This looks like some attemt to integrate an equation of motion, if that is the case this is not a good way to go about it. In that case you should integrate the second-order ODE (i.e. the two coupled first order-ODEs) and handle the evolution of the force inside the ode_research_x - function.
HTH
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