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Project: ZMF a ZFP
Views: 46
Kernel: SageMath 8.1

ODE system - interactively

System of differential equations yfekx1=dydx12y=dtdx\dfrac{y}{f}e^{-kx}-1 =\dfrac{dy}{dx} \\ \hspace{0.5 cm} -\dfrac{1}{2\sqrt{y}} =\dfrac{dt}{dx}

Initial conditions y(1)=0,t(1)=0y(1)=0, t(1)=0

# python library import ipywidgets as widgets from IPython.display import display import matplotlib.pyplot as p import numpy as np from scipy.integrate import odeint import math %matplotlib nbagg # ODE system def F(z,x,f=1/260.0,k=5.0): value = [0,0] value[0] = z[0]/f*math.exp(-k*x)-1 value[1] = -1/2*1/math.sqrt(z[0]) return value # data x xp = 1; xk = 0; dx =-0.0005 xh = np.arange(xp, xk+dx,dx) ics = (1e-15,0) # graph p.figure(figsize=(8, 5),dpi=100) ax = p.subplot(111) p.title("Energy vs. height ",fontsize=15) def graf(f,k): ax.clear() z = odeint(F,ics,xh,args=(f/10,k)) Kh = z[:,0] th = z[:,1] p.plot(th,Kh) ax.set_ylim(0, 0.5) ax.set_xlim(0, 3) p.grid(c='0.7', lw = 0.5) p.axhline(0, color='black',lw=0.75) p.axvline(0, color='black',lw=0.75) p.show() #widget f = widgets.FloatSlider(min=0.01, max=0.1, step=0.01, value=0.004, description='f(10^(-1):') k = widgets.FloatSlider(min=0, max=5, step=0.05, value=5, description='k:') widgets.interactive(graf, f=f, k=k)
WARNING: Some output was deleted.