runge-kutta

I am using the attached code to integrate a version of Fitzhugh-Nagumo model : from scipy.integrate import odeint import numpy as np import time P = {'epsilon':0.1, 'a1':1.0, 'a2':1.0, 'b':2.0, 'c':0.2} def fhn_rhs(V,t,P): u,v = V[0],V[1] u_t = u - u**3 - v v_t = P['epsilon']*(u - P['b']*v - P['c']) return np.stack((u_t,v_t)) def integrate(func,V0,t,args,step='RK4'): start = time.clock() P = args[0] result=[V0] for i,tmp in enumerate(t[1:]): result.append(RK4step(func,result[i],tmp,P,(t[i+1]-t[i]))) print "Integration took ",time.clock() - start, " s" return np.array(result) def RK4step(rhs,V

I am trying to solve for the position of a body orbiting a much more massive body, using the idealization that the much more massive body doesn't move. I am trying to solve for the position in cartesian coordinates using 4th order Runge-Kutta in python. Here is my code: dt = .1 t = np.arange(0,10,dt) vx = np.zeros(len(t)) vy = np.zeros(len(t)) x = np.zeros(len(t)) y = np.zeros(len(t)) vx[0] = 10 #initial x velocity vy[0] = 10 #initial y velocity x[0] = 10 #initial x position y[0] = 0 #initial y position M = 20 def fx(x,y,t): #x acceleration return -G*M*x/((x**2+y**2)**(3/2)) def fy(x,y,t): #y

I wish to solve the Lorentz model in Python without the help of a package and my codes seems not to work to my expectation. I do not know why I am not getting the expected results and Lorentz attractor. The main problem I guess is related to how to store the various values for the solution of x,y and z respectively.Below are my codes for the Runge-Kutta 45 for the Lorentz model with 3D plot of solutions: import numpy as np import matplotlib.pyplot as plt #from scipy.integrate import odeint #a) Defining the Runge-Kutta45 method def fx(x,y,z,t): dxdt=sigma*(y-z) return dxdt def fy(x,y,z,t): dydt

I am trying to implement the runge-kutta method to solve a Lotka-Volterra systtem, but the code (bellow) is not working properly. I followed the recomendations that I found in other topics of the StackOverflow, but the results do not converge with the builtin Runge-Kutta method, like rk4 method available in Pylab, for example. Someone could help me? import matplotlib.pyplot as plt import numpy as np from pylab import * def meurk4( f, x0, t ): n = len( t ) x = np.array( [ x0 ] * n ) for i in range( n - 1 ): h = t[i+1] - t[i] k1 = h * f( x[i], t[i] ) k2 = h * f( x[i] + 0.5 * h * k1, t[i] + 0.5 *

I would appreciate if someone can help with the following issue. I have the following ODE: dr/dt = 4*exp(0.8*t) - 0.5*r ,r(0)=2, t[0,1] (1) I have solved (1) in two different ways. By means of the Runge-Kutta method (4th order) and by means of ode45 in Matlab. I have compared the both results with the analytic solution, which is given by: r(t) = 4/1.3 (exp(0.8*t) - exp(-0.5*t)) + 2*exp(-0.5*t) When I plot the absolute error of each method with respect to the exact solution, I get the following: For RK-method, my code is: h=1/50; x = 0:h:1; y = zeros(1,length(x)); y(1) = 2; F_xy = @(t,r) 4.*exp