Why is ode45 not working when I insert the options input?

I am trying to model some functions, but it seems that ode45 is not working. However, when I get rid of 'options' when I'm calling ode45, it runs but it will not finish running. I'm still new to MATLAB, so how can I fix this issue?

%CONSTANTS

i = 6.3;

a = 1;

b = 0.83;

vNa = 115;

vK = -12;

vL = 10.5989;

simtime = [0 100];

xinit = [0, 0.4, 0.1];

%CALLING FUNCTIONS

options=odeset('RelTol',1e-9,'Refine',10);

[t,x]=ode45(@(t,x) HHModel(t,i,a,b,vNa,vK,vL,x),simtime,xinit, options);

%GRAPHS

%Membrane Potential

subplot(221); plot(t,x(:,1)); grid on;

xlabel('Time [s]'); ylabel('v');

%FUNCTIONS

function amv = am(v)

amv = ((25-v)/10)/((exp((25-v)/10))-1);

end

function bmv = bm(v)

bmv = 4*exp(-v/18);

end

function tmv = tm(v)

tmv = 1/(am(v) + bm(v));

end

function anv = an(v)

anv = ((10-v)/100)/((exp((10-v)/10))-1);

end

function bnv = bn(v)

bnv = 0.125*exp(-v/80);

end

function dx = HHModel(t,i,a,b,vNa,vK,vL,x)

amv = am(x(1));

tmv = tm(x(1));

anv = an(x(1));

bnv = bn(x(1));

dx1 = i - 120*(x(3))^3*(b - a*(x(2)))*(x(1)-vNa) - 36*(x(2))^4*(x(1)-vK)-0.3*(x(1)-vL);

dx2 = anv - x(2)*(anv - bnv);

dx3 = amv - (x(3)/tmv);

dx = [dx1;dx2;dx3];

end

Answer 1

[Jon]

Try ode15s instead, it seems to converge, you have to check if the answer makes sense

%CALLING FUNCTIONS
options=odeset('RelTol',1e-9,'Refine',10);
[t,x]=ode15s(@(t,x) HHModel(t,i,a,b,vNa,vK,vL,x),simtime,xinit,options);

[Jon]

It may be that you have a wide range of time scales in your model, that is some relatively fast dynamics and some that are relatively slow. In this case ode45 can have trouble because it needs to use such small time steps to converge that it takes a long time. For this type of system the "stiff solvers" such as ode15s are more effective.

By the way, the above call using ode15s seems to work, and give similar results with or without the call to odeset to change the default paramaters.

One other thing, regarding running with ode45 and the options set, the reason that you get no data plotted is becuase all but the first point is returned as NaN (not a number) and does not get plotted. Clearly something wrong with using that particular set of options. In anycase, seems OK with ode15s.

[Rina Dirickson]

Thank you so much!

[Jon]

Your welcome, glad this helped.