Hi everybody,
I am starting to learn how to solve ODEs analytically/numerically with
Sage, which to my understanding, implies using Maxima functions. I
followed the docu here:
http://maxima.sourceforge.net/docs/manual/en/maxima_22.html.
Now, i wanted to solve analytically the following equation:
cm*dV/dt = iM - gL*(v(t) - EL) , where cm, iM, gL and EL are parameters.
This works nicely assuming that these parameters are constant. However,
I would like to solve the equation for iM being a time-dependent
function (for example a square/sin pulse). Something like this:
cm*dV/dt = iM(t) - gL*(v(t) - EL), where iM(t) is the time-dependent
function
# define independent/dependent variables
sage: t=var('t')
sage: v=function('v',t)
# equation parameters
sage: iM, gL, EL, cm = var('iM, gL, EL, cm')
# define equation
sage: eq = diff(v,t) - 1/cm*(iM-gL*(v-EL) ) == 0
# solve it analytically
sage: desolve(de=eq, dvar=v, ivar=t, ics=[0,-65])
Then Sage returns this:-> (EL*gL*e^(gL*t/cm) + (e^(gL*t/cm) - 1)*iM - (EL
+65)*gL)*e^(-gL*t/cm)/gL
which is correct.
If I now define a function of the form:
def pulse(tonset, tdur, amp):
""" returns a square pulse as a function of t, f(t)
the pulse is defined as follows:
tonset -- start of pulse
tdur -- duration of pulse
amp -- amplitude of pulse
"""
t=var('t') # do i need this?
f(t)= amp*(sign(t-tonset)/2-sign(t-tonset-tdur)/2)
return f
I tried to define iM as a function of t
sage: mypulse = pulse(tonset =5, tdur = 10, amp =2 )
and redefined the equation (not sure if I wrote correctly
sage: eq = diff(v,t) - 1/cm*(mypulse - gL*(v-EL) ) == 0
sage: eq = diff(v,t) - 1/cm*(diff(mypulse,t) - gL*(v-EL) ) == 0 # this
is probably wrong
In either case, Sage returns the same error:
TypeError: unable to make sense of Maxima expression
'v(t)=-e^-(t*gL/cm)*(at(integrate((EL*gL+signum(t-5)-signum(t-13))*e^(t*gL/cm),t),[t=0,v(t)=-65])-integrate((EL*gL+signum(t-5)-signum(t-13))*e^(t*gL/cm),t)+65*cm)/cm'
in Sage
What I am missing here. I got a similar problem with desolve_laplace.
Should I use another ODE solver?
I got it running with Mathematica (using DSolve), but it would be great
to have it with Sage!
Thanks a lot in advance
Jose.
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