ode 45 formulation of equations in system

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gorilla3 2017년 10월 24일
I believe I have a mistake in the 1st equation of the system but I am unsure how to formulate it correctly then. Could you help?
The original equation I have troubles with is: d/dt (V_sa)= d/dt(Ca*(P1-P_ic))
Out of completion, here are the others:
  • d/dt P1 = ( (P_a_b-P1)/(R_la+0.5*R_sa_b) - (P1-P2)/(0.5*R_sa_b+R_sv) )/Ca_b
  • d/dt P2= ((P1-P2)/(0.5*R_sa_b+R_sv)-(P2-P_v)/R_lv)/(1/(k_ven*(P2-Pic-Pv1)))
  • d/dt xq= ( -xq*Gq( (( (P1-P2)/(0.5*R_sa_b+Rsv) )-q_b)/q_b ) )/tauq
  • d/dt xc= (-xc+0.3+0.3*tanh(Pa_co2/Pa_co2_b -1.1))/tau_co2
  • d2/dt xm= (eps*u-tau2*(d/dt xm)-xm)/tau1^2
I'm insecure about the 1st (V_sa), the rest should be fine. It'd be great if you could help!
This is the code: (All variables in the eq have been declared before but I won't report them here cause it's unnecessary)
F = @(t, sth) [ Ca_b*(sth(2)-P_ic);
((P_a_b-sth(2))/(R_la + 0.5 *R_sa_b) - (sth(2)-sth(3))/(0.5 *R_sa_b+R_sv))/Ca_b;
((sth(2)-sth(3))/(0.5 *R_sa_b +R_sv)-(sth(3)-P_v)/R_lv)/
1/(k_ven*(sth(3)-P_ic-P_v1)) ;
(-sth(4)+G_q*(( (sth(2)- sth(3))/(0.5 *R_sa_b + R_sv) ) -q_b )/q_b )/tau_q ;
(-sth(5) +0.3+3*tanh(Pa_co2/Pa_co2_b -1.1))/tau_co2;
(eps*u-tau2*sth(7)-sth(6))/tau1^2 ];
[t, sth] = ode45(F, [0 100], [0 0 0 0 0 0 0]);
V_sa = sth(:,1);
P1 = sth(:,2);
P2 = sth(:,3);
xq= sth(:,4);
xc= sth(:,5);
xm= sth(:,6);
xm1= sth(:,7);


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