MATLAB: Six coupled differential equations

coupledode45

New to matlab & trying to solve these equations for y(1), y(2), etc. values. I have six unknowns and six equations – why would this script fail?
function dY = rate( t,Y )
%
dY = zeros(6,1);
A51 = 26993 ;
A52 = 9894 ;
A53 = 897 ;
A54 = 1729 ;
A41 = 455 ;
A42 = 147;
A31 = 398;
A65 = 392937;
A43 = 102819;
T3 = 240E-6;
A32 = 1/T3 - A31;
C22= 10^-198;
C33= 10^-18;
R31 = 980E-9;
R13 = 1E-20;
A21 = 3094;
R36 = 240E-6;
n0=1E-20;
dY(1) = -R13*Y(1) +R31*Y(3) +A21*Y(2) +A31*Y(3) + A41*Y(4) +A51*Y(5) +C22*Y((2))^2 +C33*Y((3))^2;
dY(2) = -A21*Y(2) +A32*Y(3) +A42*Y(4) +A52*Y(5) -2*C22*(Y(2))^2;
dY(3) = R13*Y(6) -R31*Y(3) -R36*Y(3) - A31*Y(41) - A32*Y(3) + A43*Y(4) + A53*Y(5) -9*C33*(Y(3))^2;
dY(4) = -A41*Y(2) - A42*Y(4) - A43*Y(4) + A54*Y(2) +C22*(Y(2))^2;
dY(5) = -A51*Y(5) - A52*Y(5) - A53*Y(5) - A54*Y(5) + A65*Y(6);
dY(6) = R36*Y(3) - A65*Y(6) + C33*(Y(3))^2;
n0=Y(1)+Y(2)+Y(3)+Y(4)+Y(5)+Y(6);
end
* _MAIN_* 
TSPAN = [0 0 0 0 0 0 0];
t0 = 0; tf = 20E-2; 
[T,Y] = ode15('rate_eq2',TSPAN,t0,tf);
subplot(6,1,1)
plot(t,y(:,6),t,y(:,5),t,y(:,4),t,y(:,3),t,y(:,2),t,y(:,1))
legend('6','5','4','3','2','1')
title('Population different levels')

Best Answer

Your function is not the problem. You’re not calling it correctly, and you’re not using the correct solver.
Call it this way instead, and it works:
icv = ones(6,1);                                        % <== CHANGE TO APPROPRIATE INITIAL CONDITIONS
t0 = 0; tf = 2E-2; 
TSPAN = linspace(t0, tf, 150);
[T,Y] = ode15s(@rate_eq2,TSPAN,icv);
figure(1)
plot(T, Y)
grid
legend('6','5','4','3','2','1', 'Location','E')
title('Population different levels')
The ‘icv’ assignment are the initial conditions vector. If they’re all initially zero, then the solution is zero, so at least some of them have to be non-zero. You were also confusing the initial conditions and the time span arguments.
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