ode

Here scipy.integrate.odeint is called with six different standard ode problems with rtol = atol from 1E-06 to 1E-13 . I've looked at the max difference between the results at all larger tolerances minus those of the smallest, to get some kind of representation of "error". I'm curious why, for a given tolerance, one problem (D5) gives errors a million times worse than another problem (C1), even though the range in number of steps is fairly tight (within a factor of 10). The citation for the ode problems is given in the script. All problems are fairly well normalized so I'm treating rtol and

I have a von Neumann equation which looks like: dr/dt = - i [H, r] , where r and H are square matricies of complex numbers and I need to find r(t) using python script. Is there any standart instruments to integrate such equations? When I was solving another aquation with a vector as initial value, like Schrodinger equation: dy/dt = - i H y , I used scipy.integrate.ode function ('zvode'), but trying to use the same function for von Neumann equation gives me the following error: **scipy/integrate/_ode.py:869: UserWarning: zvode: Illegal input detected. (See printed message.) ZVODE-- ZWORK length

i am a newbie to python. I have a simple differential systems, which consists of two variables and two differential equations and initial conditions x0=1, y0=2 : dx/dt=6*y dy/dt=(2t-3x)/4y now i am trying to solve these two differential equations and i choose odeint . Here is my code: import matplotlib.pyplot as pl import numpy as np from scipy.integrate import odeint def func(z,b): x, y=z return [6*y, (b-3*x)/(4*y)] z0=[1,2] t = np.linspace(0,10,11) b=2*t xx=odeint(func, z0, b) pl.figure(1) pl.plot(t, xx[:,0]) pl.legend() pl.show() but the result is incorrect and there is a error message:

I am having trouble sovling the optical bloch equation, which is a first order ODE system with complex values. I have found scipy may solve such system, but their webpage offers too little information and I can hardly understand it. I have 8 coupled first order ODEs, and I should generate a function like: def derv(y): compute the time dervative of elements in y return answers as an array then do complex_ode(derv） My questions are: my y is not a list but a matrix, how can i give a corrent output fits into complex_ode()? complex_ode() needs a jacobian, I have no idea how to start constructing

I have a second order differential equation that I want to solve it in python. The problem is that for one of the variables I don't have the initial condition in 0 but only the value at infinity. Can one tell me what parameters I should provide for scipy.integrate.odeint ? Can it be solved? Equation: Theta needs to be found in terms of time. Its first derivative is equal to zero at t=0 . theta is not known at t=0 but it goes to zero at sufficiently large time. all the rest is known. As an approximate I can be set to zero, thus removing the second order derivative which should make the problem