# Problem with time span when integrating with ODE45

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Samuele Bolotta
on 8 Apr 2021

Commented: William Rose
on 11 Apr 2021

I am using ODE45 to integrate a system of differential equations and show their dynamics across 150ms. I am struggling with being precise about the time span of integration. More precisely, I have four vectors related to time:

1)

% This is the vector I pass to my ode solver as the time span of

% integration

dt = 0.25;

time = 0:dt:150;

2)

T is the output of the ODE solver and it's correctly a 1x601 vector.

3)

TimeInj, which is the time span of IInj, one of the time-dependent terms that I am interpolating.

TimeInj = 0:0.5:150; % Resulting in a 1x301 vector

4)

TimeSyn, the time span of IPSC and EPSC, the other two time-dependent terms that I am interpolating

TimeSyn = 0:0.25:150; % Resulting in a 1x601 vector

So, each vector has the same time span of 150ms, with one difference: the timestep is 0.5 for TimeInj, resulting in a 1x301 vector and 0.25 for TimeSyn, resulting in a 1x601 vector.

This is the part of my solver where I'm interpolating and integrating:

function dydt = myode(T,Vmnh,TimeInj,IInj,TimeSyn,Gsyn)

..........................

%% Interpolate currents

IInj = interp1(TimeInj,IInj,T);

IPSC = interp1(TimeSyn,IPSC,T);

EPSC = interp1(TimeSyn,EPSC,T);

%% Integration

dydt = [((1/Cm)*(IInj-(INa+IK+Il+IPSC+EPSC)));

alpham(Vmnh(1))*(1-Vmnh(2,1))-betam(Vmnh(1))*Vmnh(2,1);

alphan(Vmnh(1))*(1-Vmnh(3,1))-betan(Vmnh(1))*Vmnh(3,1);

alphah(Vmnh(1))*(1-Vmnh(4,1))-betah(Vmnh(1))*Vmnh(4,1)];

However, as you can see from the image I attached, the timespan for Current IInj and Synaptic Conductances EPSC and IPSC is correctly 150, while the one for the first and four subplot is not correct and has lots of NaN values starting from a certain point. I think I'm doing something wrong with either the time steps or I'm not respecting some rules with the time spans. Thanks!

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William Rose
on 8 Apr 2021

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