MATLAB: How to call multiple functions in ode 45

functionode45recall

I'm trying to solve 2 systems of differential equations using ode45, however I get the error code:
Error using odearguments (line 21) When the first argument to ode45 is a function handle, the tspan argument must have at least two elements.
Error in ode45 (line 115)
    odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
Error in CBF_2006_f_v1 (line 49)
    [ABP,P1,P2,xq,xm,xc,xm1,Cav] = ode45(@vsa, @aut, tspan, var0);
There are 2 systems: 4 equations each. The unknowns are (V_sa,P1,P2,xq,xm,xc,xm1,Cav), all the rest are parameters that have been declared at the beginning of the code.
The code main code that recalls the functions is:
%Parameter declaration .... (Rsa,V_sa_b,P_ic ...)
%%Diff eq system
      ABP= linspace(40,170,131);
      delta=deltaCa_p;
      for i=1:1:length(ABP)
      tspan=[0 100];
      var0=[12; 97.6; 49.67; 0; 0; 0; 0; 0.205];
      [ABP,P1,P2,xq,xm,xc,xm1,Cav] = ode45(@vsa, @aut, tspan, var0);
      end
The 2 functions are stored in separate files and their code is:
function dvdt = vsa(ABP,var,delta,R_la,R_sa_b,V_sa_b,R_sv,P_ic,P_v,k_ven,P_v1)
dvdt = [(0.5*delta*(1- ((cosh(4*(var(6)+var(5)-var(4))/delta))-1)/(cosh(4*(var(6)+var(5)-var(4))) +1)))*(var(2)-P_ic) + var(8)*(( (ABP(i) -var(2))/(R_la+0.5*(R_sa_b*(V_sa_b/var(1))^2)) - (var(2)-var(3))/(R_sv+0.5*(R_sa_b*(V_sa_b/var(1))^2)) - (var(2)-P_ic)*(0.5*delta*(1- ((cosh(4*(var(6)+var(5)-var(4))/delta))-1)/(cosh(4*(var(6)+var(5)-var(4))) +1))))  /var(8)) ;
    ( (ABP(i) -var(2))/(R_la+0.5*(R_sa_b*(V_sa_b/var(1))^2)) - (var(2)-var(3))/(R_sv+0.5*(R_sa_b*(V_sa_b/var(1))^2)) - (var(2)-P_ic)*(0.5*delta*(1- ((cosh(4*(var(6)+var(5)-var(4))/delta))-1)/(cosh(4*(var(6)+var(5)-var(4))) +1))))  /var(8);
                  ((var(2)-var(3))/(0.5 *(R_sa_b*(V_sa_b/var(1))^2) +R_sv)-(var(3)-P_v)/R_lv)*1/(1/(k_ven*(var(3)-P_ic-P_v1))) ;
                      0.5*delta*(1- ((cosh(4*(var(6)+var(5)-var(4))/delta))-1)/(cosh(4*(var(6)+var(5)-var(4))) +1))] ;
V_sa= var(:,1);
P1= var(:,2);
P2 = var(:,3);
Cav=var(:,8);
xq= var(:,4);
xc= var(:,5);
xm= var(:,6);
xm1= var(:,7);
dvdt=[V_sa;P1;P2;Cav; xq;xc;xm;xm1;Cav];
end
and
    function dxdt= aut(ABP,var,G_q,R_sa_b,V_sa_b,Pa_co2,Pa_co2_b,tau_co2,eps,u,tau2,tau1)
    dxdt=[                                     (-var(4)+G_q*( ( (var(2)- var(3))/(0.5 *(R_sa_b*(V_sa_b/var(1))^2) + R_sv) ) -q_b /q_b) )/tau_q ;
                                               (-var(5) +0.3+3*tanh(Pa_co2/Pa_co2_b -1.1))/tau_co2;
                                                                  var(7);
                                                                     (eps*u-tau2*var(7)-var(6))/tau1^2 ];
    V_sa= var(1);
    P1= var(2);
    P2 = var(3);
    xq= var(4);
    xc= var(5);
    xm= var(6);
    xm1= var(7);
    dxdt=[P1;P2;xq;xc;xm;xm1];
    end
Could you please help me find the mistakes?

Best Answer

I would nest them into one function:
bothfcns = @(ABP, var) [@(ABP,var) vsa(ABP,var,delta,R_la,R_sa_b,V_sa_b,R_sv,P_ic,P_v,k_ven,P_v1); @(ABP,var) aut(ABP,var,G_q,R_sa_b,V_sa_b,Pa_co2,Pa_co2_b,tau_co2,eps,u,tau2,tau1)];
Then use ‘bothfcns’ as the function argument to ode45.
NOTE — I cannot run your code to test this, so I am listing this as UNTESTED CODE.
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