MATLAB: Errors using ode45: “Not enough input arguments”. I am not sure what this errors try to tell me, I performed this type of problems before using ode45 and never ran into such error. I have carefully checked the codes. Any suggestions/explanation

notenoughinputargumentsode45systemsofodes

%%solve_ODEs_system_CancerECM
function solve_ODEs_system_CancerECM
%  ouput is concentration of collagen fibers and enzyme MMPs in the ECM
%  describe degradation of ECM due to MMPs
%  system of ODEs are obtained and further derived from toma a.-a novel
%  method for simulating the ECM in models of tumor growth
 %%Description of Input and output parameters or varibales:
    %%Input
    % Dm : diffusion coefficient of enzyme MMPs
    % alpha_m: decay coefficient of MMPs
    % beta_m: production rates of MMPs
    % alpha_f: uptake parameter of ECM 
    % beta_f: remodeling parameter of ECM
    % m1: concentration of MMPs
    % m2: 1st order derivative of m1
 %%Units of Input and output parameters or varibales:
 %%Setup initital conditions for the ODE solver
clear;
f_0       = 1;
m1_0      = 0.1;
m2_0      = 0.1;
f0_and_m0 = [f_0; m1_0; m2_0];
 %%Define the t range and increments
t0 = 0;
tf = 10;
t = t0:0.01:tf;
 %%Call the ODE solver
[t,y]=ode45(@ODEs_system_CancerECM,t,f0_and_m0); 
 %%Retrive values for each variables from output solution
f  = y(:, 1);
m1 = y(:, 2);
m2 = y(:, 3);
 %%Figure 1: Plot the results of T vs.  V 
figure(1)
plot(t,f)
title('ECM density vs. time')
xlabel('time')
ylabel('ECM density')
 %%Figure 2: Plot the results of Fi vs.  V 
figure(2)
plot(t,m1,'r--',t,m2,'bs')
legend('MMPs concentration','[MMP] rate of change','location','best')
title('[MMPs] vs. time')
xlabel('time')
ylabel('[MMP]')
    %%Define system of ODEs   
    function dydt = ODEs_system_CancerECM(t,f,m1, m2)
        %%All parameters (using tentative values for now) --> UPDATE
        % Dm and alpha_m, and even beta_m can be obtained from literature
        Dm      = 0.08 ; %toma
        alpha_m = 0.02 ;
        beta_m  = 0.01  ;
        % alpha_f and beta_f can be approximated following parameter
        % estimation methods (lsqcurvefit, for example)
        alpha_f = 0.01 ;
        beta_f  = 0.015  ;
        %%Define ODEs system
        d_f_dt  = -alpha_f*f*m1 + beta_f*f;
        d_m1_dt = m2;
        d_m2_dt = (1/Dm)*m2 + (alpha_m/Dm)*m1 - (1/Dm)*beta_m;
        %%Return results as column vector
        dydt     = zeros(3,1);
        dydt(1,1)= d_f_dt;
        dydt(2,1)= d_m1_dt;
        dydt(3,1)= d_m2_dt;
    end
end

Best Answer

You call
[t,y]=ode45(@ODEs_system_CancerECM,t,f0_and_m0);
which implies that ODEs_system_CancerECM is to be called with t and y arguments over a timespan of t, with initial conditions f0_and_m0
You define
    function dydt = ODEs_system_CancerECM(t,f,m1, m2)
which expects to be passed 4 arguments.
I speculate that you want
      function dydt = ODEs_system_CancerECM(t,fm)
        f = fm(1); m1 = fm(2); m2 = fm(3);
Related Question