I am a quite new user of sage, and -up till now- I am really amazed by it power and by its user-friendliness and intuitiveness, I am really happy.
I came up with a problem in solving numerically systems of ode's.
the things are as follows:
I solve a system of ode's (using "desolve_system_rk4") let's say with dependent variables x,y,z and dependent variable t. so, theoretically I end up with 3 functions of time x(t),y(t),z(t). In fact I only have a list of 'points' [t,x(t),y(t),z(t)] for a certain time-grid that I can choose.
now, suppose I have to find many other functions of time (actually a matrix with entries as function of time, let us call it A(t)), whose dynamics (i.e. the coefficients of the ode) depends on x(t) y(t) z(t), how can I give sage the input x(t) y(t) z(t)? I have only a bunch of points.
I tried the obvious way, which is to interpolate the points with "spline", but then the solver of the ode's (for A(t)) doesn't work anymore, it gives me an error of floating precision.
the other way, which actually worked, but to me it seems a bit sloppy, is to solve directly the entire system of x,y,z AND the matrix of functions A(t). This gives the answer, but it seems to me a bit unelegant that I have to recalculate the x,y,z which I already know..can you see the point?
thank you d-